Coherent control of NV- centers in diamond in a quantum teaching lab
Vikas K. Sewani, Hyma H. Vallabhapurapu, Yang Yang, Hannes R. Firgau, Chris Adambukulam, Brett C. Johnson, Jarryd J. Pla, Arne Laucht
CCoherent control of NV − centers in diamond in a quantum teaching lab Vikas K. Sewani, ∗ Hyma H. Vallabhapurapu, Yang Yang, Hannes R. Firgau, Chris Adambukulam, Brett C. Johnson, Jarryd J. Pla, and Arne Laucht † Centre for Quantum Computation and Communication Technology,School of Electrical Engineering and Telecommunications,UNSW Sydney, Sydney, New South Wales 2052, Australia School of Electrical Engineering and Telecommunications,UNSW Sydney, Sydney, New South Wales 2052, Australia Centre for Quantum Computation and Communication Technology,School of Physics, University of Melbourne, Melbourne, Victoria 3010, Australia
The room temperature compatibility of the negatively-charged nitrogen-vacancy (NV − ) in dia-mond makes it the ideal quantum system for a university teaching lab. Here, we describe a low-costexperimental setup for coherent control experiments on the electronic spin state of the NV − center.We implement spin-relaxation measurements, optically-detected magnetic resonance, Rabi oscilla-tions, and dynamical decoupling sequences on an ensemble of NV − centers. The relatively shorttimes required to perform each of these experiments ( <
10 minutes) demonstrate the feasibility of thesetup in a teaching lab. Learning outcomes include basic understanding of quantum spin systems,magnetic resonance, the rotating frame, Bloch spheres, and pulse sequence development.
I. INTRODUCTION
The arrival of the second quantum revolution – tech-nologies that exploit coherent quantum phenomenon,such as quantum computation, quantum communication,and quantum sensors – has elevated quantum physicsfrom fundamental research to an applied science [1]. Athorough understanding of quantum mechanics is notonly desirable but quite often demanded of universitygraduates entering the job market in this field. Theoret-ical skills are easily taught with pen and paper, by deriv-ing analytical solutions, or with a few lines of computercode running numerical simulations, but real hands-onexperience in manipulating a quantum system is, unfor-tunately, much more difficult to convey. This is partlydue to the sensitivity of quantum systems to environ-mental disturbances that often demands operation atcryogenic temperatures or inside vacuum chambers, andpartly due to the high cost of specialized equipment.The NV − center in diamond is an especially advanta-geous quantum system for a teaching lab as its electronspins can be initialized, controlled, and read out at roomtemperature in ambient atmosphere [2], strongly reduc-ing the complexity of the experimental apparatus. Henceit has previously been recommended for teaching lab se-tups for magnetic resonance and magnetometry [3], andis even available as a commercial system [4]. However,coherent control of the electronic spin state has not beendemonstrated in a convenient and cost-effective fashion.Here, we describe a teaching lab setup that allows stu-dents to learn about fundamental concepts of quantummechanics by coherently controlling the electronic spinstate of the NV − center in diamond. In fact, studentscan adapt and design their own control sequences andexperiments. The presented setup is robust to its envi-ronmental conditions, such that it can even be operatedin broad daylight on a normal desk, and does not requirethe carefully controlled environment of a research labo- ratory. Finally, the setup can be assembled for a totalcost of less than USD 20k.This paper is organized as follows: In the proceed-ing section (Section II) we will give an overview of thelearning outcomes that can be conveyed with these ex-periments. In Section III we will give a short introduc-tion to the NV − center in diamond, explaining how ini-tialization, control, and readout of the electronic spinstates is achieved. Section IV provides a detailed de-scription of the experimental setup. More specifically,Subsection IV A describes the diamond sample we use,Subsection IV B describes the optical part of the setup,Subsection IV C describes the equipment required for de-livery of a microwave (MW) field, and Subsection IV Ddescribes the signal detection scheme using a lock-in am-plifier in combination with digital pulse sequences. Fi-nally, Section V describes the various experiments thatcan be conducted with this setup, with special attentionto the quantum mechanical concepts that these experi-ments convey. II. LEARNING OUTCOMES
At UNSW Sydney, the experiments described belowhave been incorporated into a course targeted at the 4th-year undergraduate level. At the time of writing, we havethus far run the course for 1 semester where students havebeen able to successfully perform all experiments, anddemonstrate the learning outcomes. A total of 9 stu-dents were enrolled in that semester, and were dividedinto groups of 2-3. Each group had 2 hours per weekto perform the experiments, for 4 weeks in total. Dueto the number of groups, two identical setups were builtand were operated simultaneously during the lab times.During the course of the labs, it was essential for stu-dents to demonstrate links between experimental results,and both quantitative and qualitative understanding of a r X i v : . [ phy s i c s . e d - ph ] A p r quantum theory. More specifically, these labs encouragestudents to achieve the following:1. Understand the NV − center structure, the spin ini-tialization and readout procedure, and the spectralfeatures.2. Incrementally develop pulse sequences with increas-ing complexity, i.e. starting from purely opticalspin-dynamics for T measurements, to complexdynamical decoupling sequences for T measure-ments.3. Understand the rotating frame, magnetic reso-nance, two-axes control, and be able to follow thespin orientations along the Bloch sphere duringpulse sequences.4. Understand the incremental steps required to im-plement dynamical decoupling pulse sequences,such as finding a spin transition in the spectrum,performing Rabi oscillations, and calibrating π -pulse lengths. Due to the short experimental runtimes, students can often perform all experimentsin a single 2-hour lab once they have obtained theexpertise.Concepts demonstrated with these experiments aretransferable to other quantum systems [5], like elec-tron spin qubits confined to donors or quantum dots [6,7], nuclear spin qubits [8], superconducting qubits [9],atoms in ion traps [10], and magnetic resonance imaging(MRI) [11]. Literature that is readily available on thesesystems frequently benchmarks quantum devices usingthe same methods as described below. Performing suchexperiments has, up until now, often only been availableto research students in an expensive research lab. III. THE NV − CENTER IN DIAMOND
The NV − center in diamond consists of a substitu-tional nitrogen atom adjacent to a vacant lattice site, asschematically shown in Figure 1(a). It can exist along 4different crystallographic orientations ([111], [1¯1¯1], [¯11¯1],and [¯1¯11]), which are in principle equivalent, but leadto different alignments of their NV − center axes with re-spect to an externally applied static or oscillating mag-netic field.The static Hamiltonian of the NV − center groundstate, neglecting any interactions with nuclear spins orspin-strain interactions, and assuming that the NV − -axisis oriented along the z-direction, is given by: H = D S + γ e B S u , (1)where D = 2 .
87 GHz is the zero-field splitting of theground state, γ e = 28 GHz/T is the electron gyromag-netic ratio, B is the magnetic field applied along an ar-bitrary direction (cid:126)u , and S x , y , z ,u are the spin matrices for FIG. 1. (a) Atomic structure of the NV center in diamondwith a substitutional nitrogen atom (red) adjacent to a vacantlattice site (transparent). The depicted NV center is orientedalong the [111] lattice direction, however due to the tetrahe-dral structure of the crystal lattice, the NV center axis canalso be oriented along the [1¯1¯1], [¯11¯1], and [¯1¯11] lattice direc-tions. (b) Energy levels and transitions of the NV − . The blueshaded regions represent continua of orbital and vibrationalstates. Thick black arrows represent high probability tran-sitions, while thinner arrows represent low probability tran-sitions. The grey shaded region represents the intermediatesinglet states. S = 1 along the x,y,z-axes and the (cid:126)u -direction [12]. Inthis paper, we will treat H in units of frequency, as thisis more relevant for experiments.In order to achieve magnetic spin resonance and co-herent control, we need an oscillating magnetic field B that induces transitions between the spin sub-levels. Forexample, a resonant B field enables us to controllablyrotate the ground state spin states from | (cid:105) g to |± (cid:105) g and back (termed Rabi oscillations). This field is usu-ally created at the position of the NV − centers using aMW signal generator and an antenna (discussed furtherin Section IV). We include the oscillating magnetic fieldin the Hamiltonian as a time-dependent term given by: H = γ e B cos(2 πν t )S v , (2)where B is the magnitude of the oscillating magneticfield at frequency ν applied along an arbitrary direction (cid:126)v , and S v is the spin matrix along the (cid:126)v -direction.Due to the exact way the sample is mounted in thesetup, there can be an angle between the static mag-netic field B , the oscillating magnetic field B , and thedirection in which the crystal field acts (defined as thez-direction in Equation 1), as for example indicated inFig. 4(d). In fact, due to the 4 possible orientations ofthe NV − center axis in the tetrahedral crystal, NV − swith different orientations will, intrinsically, have differ-ent Zeeman splittings and Rabi frequencies.The energy levels and transitions of the ground, excitedand singlet states of the NV − center within the diamondbandgap are depicted in Figure 1(b). The ground state | g (cid:105) and excited state | e (cid:105) are both spin-carrying stateswith S = 1. In | g (cid:105) at B = 0 T, the |± (cid:105) g states are (a) (b) SMA d1d2l2l1 l2g
Top Layer CopperBottom Layer Copper (d)2 2.5 3Microwave Frequency (GHz)-0.9-0.6-0.30 N o r m a li ze d S ( d B ) | B | ( µ T ) N o r m a li ze d S ( d B ) | B | ( µ T ) (e)(c)Electronics Optics FIG. 2. (a) Electronics setup. (b) Optics setup. (c) CAD drawing of the PCB antenna designed to deliver the oscillatingmagnetic field B to the NV − spins. The geometric parameters are d d . l . l . g = 0 . μ mof copper thickness on each side. (d) Magnitude of the magnetic field | B | at +24 dBm of excitation at 2.57 GHz, around the1 mm hole. Simulations were performed in CST Microwave Studio. (e) Comparison of simulated (blue) and measured (red)power reflected from the antenna (S ), and simulated magnetic field magnitude | B | (black). at ν D = 2 .
87 GHz higher energy than the | (cid:105) g statedue to the zero-field splitting D . Green laser light at λ = 520 nm or λ = 532 nm can excite the NV − elec-trons from the ground state | g (cid:105) into the continuum oforbital and vibrational excited states (upper blue shadedregion) above the excited state | e (cid:105) (referred to as off-resonant excitation), from which they rapidly relax into | e (cid:105) . From there the electrons can decay radiatively, eitherdirectly to | g (cid:105) by emitting a photon at λ ZPL = 637 nminto the zero-phonon-line (ZPL), or by simultaneouslyemitting a phonon and a photon of longer wavelengthinto the phonon-sideband (PSB). In either case, thereis a high probability that the spin state of the electronwill remain unchanged during this optical cycling, dueto spin-conservation. Alternatively, the NV − electronscan decay non-radiatively via the singlet state | s (cid:105) . Decayfrom | e (cid:105) to | s (cid:105) is favoured by the |± (cid:105) e states comparedto the | (cid:105) e state (as indicated by the thicker arrow), anddecay from | s (cid:105) to | g (cid:105) favours the | (cid:105) g spin orientation of | g (cid:105) . Overall, these transition rules have 2 effects:1. Electrons cycling between the | (cid:105) g and | (cid:105) e states emit ∼
30% more photons than those cycling between the |± (cid:105) g and |± (cid:105) e states. This provides a readout mecha-nism for the ensemble electronic spin state.2. With continuous laser excitation, electrons cycling be-tween |± (cid:105) g and |± (cid:105) e states will over time populate the | (cid:105) g state. The electrons can therefore be spin-initializedinto the | (cid:105) g state [2]. IV. EQUIPMENT
In this section we provide details about the experi-mental setup. All optical and electrical components werepurchased off-the-shelf, while the printed circuit boardsfor the antenna [see Fig. 2(c)] and the laser current driver(more information in Appendix B) can be commerciallymanufactured (Gerber files on request). While the dia-mond samples used for these experiments are not com-mercially available, the company element six offers dia-mond samples in their online shop that work without anysample processing. A detailed list of all parts with partnumbers and recent prices can be found in Appendix A.
A. Diamond sample
The diamond sample is a single crystal Type 1b high-pressure, high-temperature (HPHT) diamond, electron-irradiated with a density of 10 /cm , and annealed at900 ◦ C for 2 hours. The top facet is oriented perpen-dicular to the [111] direction. All experiments measurethe photoluminescence (PL) from a large ensemble ofNV − centers with all four possible orientations. An un-processed chemically-vapour-deposited (CVD) diamondsample (available from element six ) is also sufficient forthe experiments described herein and will contain a mea-surable number of NV − centers. The electron irradiationsignificantly increases the PL intensity but reduces thecoherence times which can be a limiting factor for somemore advanced measurement protocols. B. Optical setup
The setup was designed with the goal of keeping theoptical components to a minimum while ensuring easeof alignment. This way, the setup can be easily in-corporated onto a small optical breadboard (ThorlabsMB3045/M) for portability, and fully covered with anenclosure (Thorlabs XE25C7/M) to constrain laser scat-tering.A schematic of the optics part of our setup is shownin Figure 2(b). We use a single mode, fiber-coupled520 nm green laser diode (Thorlabs LP520-SF15) as ourexcitation source. The beam is first collimated usingan aspheric lens (Thorlabs C280TMD-A), and then re-flected off a 550 nm long-pass dichroic mirror (ThorlabsDMLP550) and onto a microscope objective (OlympusMS Plan 50x/0.80NA). The objective lens focuses thelaser to a focal spot of ∼ μ m on the diamond sample,which results in an excitation volume over which B and B field are both relatively constant. The diamond sam-ple is mounted on a 3-axis translation stage (ThorlabsMBT616D/M). Between the objective lens and the di-amond sample, we place a printed circuit board (PCB)MW antenna to create the strong oscillating magneticfield ( B field) for spin control. The antenna structureincludes a 1 mm diameter hole, through which both theexcitation laser, and the PL emission from the diamondsample can pass. The design of the antenna is discussedin more detail in Section IV C.The PL signal from the diamond sample is transmittedthrough the dichroic mirror and into the detection partof our setup. Here, a flip-mirror (Thorlabs PF10-03-P01 on Thorlabs TRF90/M) allows the signal to follow oneof two paths:1. Through an achromatic doublet (Thorlabs AC254-125-A) onto a CMOS camera (Thorlabs DCC1545M)that allows for alignment of the sample and focusing ofthe laser using the 3-axis stage. A 600 nm long pass fil-ter (Thorlabs FEL0600) and a 900 nm short pass filter(Thorlabs FES0900) can be added here to view the PLsignal instead of residual laser light.2. Via two silver-coated mirrors (Thorlabs PF10-03-P01)on separate kinematic mounts (Thorlabs KM100) andthrough an aspheric lens (Thorlabs C260TMD-B) into a50 μ m multi-mode fiber (Thorlabs M42L01) that guidesthe light to a photodiode (Thorlabs DET025AFC/M) fordetection. A 600 nm long pass filter (Thorlabs FEL0600)and 900 nm short pass filter (Thorlabs FES0900) areplaced in this path to ensure that only the NV − PL isdetected.
C. Microwave setup
A block diagram of the electronics part of our setupis shown in Figure 2(a). The block labeled ‘MicrowaveSource & Amp’ is discussed in this section. First, a PCcommunicates with the MW source (SignalCore SC800)to set the MW frequency between 0-6 GHz. The MWsignal is fed into an I/Q modulator (Texas InstrumentsTRF370417EVM). The ‘I’, or ‘in-phase’, input of themodulator controls the amplitude of a MW signal thathas the same phase as the input MW signal. The ‘Q’,or ‘quadrature’, input controls the amplitude of a MWsignal that is 90 ◦ phase shifted. The output of the mod-ulator is the sum of these signals. For our experiments,it is sufficient to restrict the I and Q inputs to high/lowsignals (TTL high or low), which enable or disable the Iand Q signal components. The modulator’s output istherefore either a signal that is in-phase with the in-put MW signal (I high, Q low), 90 ◦ out phase (I low,Q high), or 45 ◦ out of phase (I high, Q high). Themodulator’s output is then amplified by a MW ampli-fier (ZQL-2700MLNW+) to a MW power of +24 dBm(251 mW), and transmitted to the PCB antenna [shownin Figure 2(c)] with via a coaxial cable with SMA con-nectors on both ends.The antenna is designed to produce the oscillatingmagnetic field B at the position of the NV − centers.Figure 2(c) shows our antenna design with all geometri-cal parameters, adapted from Ref. [13]. The antenna wasdesigned and simulated in-house using Eagle CAD and
CST MW Studio , respectively, and manufactured com-mercially by the PCB manufacturer
Seeed Studio . Theantenna geometry is referred to as a loop-gap resonator,where the ‘loop’ in our case is a through hole, near whichwe can have a strong oscillating B field in the directionperpendicular to the plane of the PCB as shown in Fig-ure 2(d). This hole also allows for both the excitationlaser and the PL of the diamond sample to pass throughthe PCB.Simulations indicate that the antenna has a resonanceat 2.57 GHz, given by the S -dip shown by the bluecurve in Figure 2(e). In the manufactured PCB, we mea-sure the resonant S -dip to be at ∼ B = 306 μ T (black curve), whichwould result in an electron spin Rabi frequency of Ω R = γ e B ≈ . B in magnitude( (cid:107)∇ B (cid:107) = 0 . μ T/ μ m at +24 dBm of excitation power). D. Pulsing sequences and lock-in detection
As discussed in Section III, the NV − center emits ∼
30% more photons when decaying from the | (cid:105) e statescompared to the |± (cid:105) e states. Under experimental con-ditions, where we collect emission from the four differentNV − orientations simultaneously, and spin control of theensemble is far from ideal, the contrast of the spin signalis limited to a few percent. It is possible to extract thespin signal by using a power-stabilized laser source andsufficient averaging. However, to achieve a more robustimplementation for a teaching lab, we employ a lock-inamplifier.The operation of a phase-sensitive lock-in amplifier iswell-known, and described in Ref. [15]. Given a refer-ence frequency, the lock-in amplifier will make a phasesensitive measurement of signals present exactly at thatfrequency, with a bandwidth as narrow as 0.01 Hz (se-lectable). If the signal of choice can be modulated at thereference frequency, the lock-in amplifier can extract itwith a good signal-to-noise ratio (SNR) from large back-ground signals at other frequencies. For example, in anexperiment where laser excitation provides a PL signalfrom an ensemble of NV − centers, and a resonant MWsource drives the spin from the | (cid:105) g state to the |± (cid:105) g states, the spin signal can be extracted with a lock-inamplifier when the MW field is amplitude or frequencymodulated at the reference frequency, while any DC sig-nal is rejected.The experiments are clocked and triggered by a PulseBlaster ESR Pro 250 pulse pattern generator, that canbe programmed to generate TTL pulse sequences on upto 24 channels. For the experiments described here, werequire 4 channels: • ‘CH0’ provides the reference frequency to a phasesensitive lock-in amplifier (Ametek 5210 or alterna-tively Stanford Research Systems SR830). • ‘CH1’ pulse-modulates the 520 nm laser diode viaan in-house designed high-speed current source (discussed in Appendix B). • ‘CH2’ provides the I input for the I/Q modulator(discussed in Section IV C). • ‘CH3’ provides the Q input for the I/Q modulator.We perform our experiments by programming pulsesequences onto the 4 channels, keeping in mind that weonly modulate the signals at the lock-in reference fre-quency that we are interested in detecting (except for the T measurements in Section V A). Each experiment be-low has a specific pulse sequence associated with it. Thesoftware programming of each pulse sequence is done ona PC using Matlab, and the pulse blaster is configuredto generate the corresponding TTL pulses via USB serialinterface. V. EXPERIMENTSA. Spin initialization and readout - T measurement At room temperature, without any laser, MW exci-tation, or external magnetic fields, the NV − spins arecompletely depolarized and the spin states are equallypopulated, as described by a Boltzmann distribution for atwo-level system with a 2.87 GHz level splitting at 300 K.Thus, all experiments discussed in this paper will startwith spin initialisation via an optical pulse as describedabove. As discussed in Section III, electrons decaying viathe | s (cid:105) state will be initialized into the | (cid:105) g state with ahigh probability. Hence, continuous 520 nm laser exci-tation, and therefore repeated optical cycling of the dy-namics discussed in Section III, will result in the ensemblebeing initialized into the | (cid:105) g state.Readout of the NV − spin states at the end of the ex-periment relies on the same process. A laser pulse is usedto excite the NV − centers to the | e (cid:105) state. As relaxationvia the | s (cid:105) state is more likely for the |± (cid:105) e state than forthe | (cid:105) e state, the | (cid:105) e state will result in a larger numberof photons being detected at the wavelengths of the ZPLand PSB.The spin T decay time gives an idea of how long thespins remain in the prepared state, before longitudinalrelaxation into a Boltzmann-distributed population oc-curs. Note, that a T experiment measures the spin de-cay time only, and is not sensitive to any dephasing ofthe system. There are two methods to measure the spin T decay time:1. By initializing the spins into the | (cid:105) g state using alaser pulse, leaving them to relax for a time τ delay ,and then measuring the resultant spin populationwith a second laser pulse. This is a fairly sim-ple measurement that requires no MW control andworks at zero B magnetic field. Furthermore, itresults in a signal from all members of the ensem-ble, irrespective of the orientation of the NV − axes. (a) (b) 0 2 4 60.3750.385 T = 1.64 0.25 msi i r 0.3800.390 FIG. 3. (a) Pulse sequences programmed to measure the spin T decay of the NV − ground state, and a multi-spin representationshowing the set of pure spin state vectors that constitute the NV − spin ensemble at selected times along the pulse sequence. τ ref =15 ms, τ laser =5 μ s, and τ delay is varied. (b) NV − center T decay measured with lock-in detection. The total measurementtime is ∼
2. By additionally using a resonant MW pulse to co-herently invert the spin population before the decayperiod τ delay . At non-zero B field, this methodallows the selection of a specific spin transitionand measurement of its corresponding T time.However, due to the different orientations of theNV − center axes with respect to the B and B fields (see also Section III), a MW pulse will not beresonant with all the defects or lead to non-perfectinversion, producing a partial initialization of thespin ensemble and resulting in a smaller signal.We choose the first method for the teaching labs. Thismethod results in a stronger signal, and allows the intro-duction of spin initialization and readout independent ofthe concept of MW spin control.Figure 3(a) describes the pulse sequence to implementthe all-optical T measurement. CH0 sets the referencesignal for the lock-in amplifier, while CH1 defines thelaser pulse sequence. There are two initialization laserpulses in the sequence [denoted ‘i’ in Figure 3(a)], one atthe beginning of each half-cycle. As they are separatedby a π -phase shift with respect to the lock-in reference(CH0), the lock-in detection will cancel out this signalunder the condition that τ ref (cid:29) T . The second initial-ization pulse is followed by a readout laser pulse (denoted‘r’) of the same length, after a variable delay τ delay . Thesignal caused by the readout pulse is dependent on the T process, however since this laser pulse is only present inthe second half-cycle of the reference, the readout pulsewill additionally result in the detection of a PL signalthat is independent of T (i.e. a background signal). InFigure 3(b), we show the corresponding measurement.The signal decreases from 0.391 mV to 0.374 mV witha time constant of T = 1 . ± .
25 ms. The 4.3%change in signal corresponds to the spin decay from the | (cid:105) g state to the Boltzmann-distributed population. The 0.374 mV offset originates from the spin-independent PLsignal caused by the readout pulse being present in onlyone of the two half-cycles. B. Optically detected magnetic resonance andZeeman effect
As discussed in Section III, an oscillating magnetic field B can be used to controllably rotate the NV − ground-state electronic spin. To demonstrate this, we employanother channel of the Pulse Blaster (denoted ‘CH2’) topulse-modulate the output of the MW source and cre-ate a sequence of oscillating B pulses, as shown in Fig-ure 4(a) (see also Sections IV C and IV D for details of thesetup). We start by measuring the spin transition spec-trum of the NV − center ensemble in zero magnetic field.As before, an initial laser pulse is used to initialize theNV − into the | (cid:105) state. A subsequent MW pulse of fixedlength τ mw ( (cid:29) T ∗ ) then attempts to rotate the spins.When the MW frequency is equal to the | (cid:105) g ←→ |± (cid:105) g transition frequency, we rotate the spins about the +Xaxis [16]. The next laser pulse will serve as the readoutpulse. This procedure is referred to as optically detectedmagnetic resonance (ODMR), as the optical signal is re-duced in magnitude when the spins are rotated from the | (cid:105) g state into the |± (cid:105) g state. Using a lock-in amplifier,the resonance condition will result in a large, positivemagnitude reading, which represents the absolute valueof the change in signal under resonance. Out of resonancethe MW pulses have no effect on the lock-in magnitude.Figure 4(b) shows the zero magnetic field ODMR spec-trum. The main peak is centered at D = 2 .
87 GHz, witha spin-strain splitting E = 7 MHz which lifts the de-generacy of the | (cid:105) g ←→ |± (cid:105) g transition. Additionally,the side peaks visible are a result of hyperfine interac-tion ( A = 128 MHz) of the subset of NV − spins that are FIG. 4. (a) Pulse sequence to perform pulsed-ODMR spectroscopy and Rabi oscillations, and multi-spin representation showingthe set of pure spin state vectors on a Bloch sphere for NV − centers of one particular orientation (i.e. all spins are resonantwith the MW frequency). τ ref = 2 . τ laser = 5 μ s, τ padding = 1 μ s, τ mw = 5 μ s for pulsed-ODMR, and τ mw is varied forRabi oscillations. Laser and MW pulses sequences (CH1 and CH2) are repeated 500 times within each half-cycle to increasethe signal strength. (b) Zero-field pulsed-ODMR spectrum. The main ODMR peak is centered at D = 2 .
87 GHz. The splitting E = 7 MHz is a result of lifting the |± (cid:105) g degeneracy due to a spin-strain interaction (corresponding term not included inEq. 1). The smaller side peaks are split by A = 128 MHz, and are due to the hyperfine interaction of the NV − centers coupled toa nearest neighbor C nucleus with a nuclear spin of ± / ∼ B magnitudes follow B A0 < B B0 < B C0 . The total measurement time is ∼ B C0 at the resonant frequency of the MW antenna [compare Figure 2(d)]. The peak fits to aLorentzian centered at ν ODMR = 2 .
49 GHz and linewidth Γ
FWHM = 14 . ν ODMR = 2 .
49 GHz. Measurement time is ∼ also coupled to a nearest neighbor C nucleus. The sidepeaks are ∼ .
3% of the center peak intensity, which cor-responds to the probability of finding a C nucleus nextto an NV − site.Figure 4(c) shows further ODMR spectra recorded forarbitrary magnetic fields B A0 , B B0 , B C0 , introduced byplacing a permanent magnet in the proximity of the di-amond crystal. The energy splitting of the |± (cid:105) g state depends on the orientation of the B field with respectto the NV − axis, allowing us to distinguish between the4 different NV − orientations in our ODMR spectra, andresolving a total of 8 transitions for the field strengths B A0 and B C0 , and 6 transitions in B B0 due to an overlapof 2 pairs of transitions (see also Section III). FIG. 5. (a) Dynamical decoupling pulse sequence, with one refocusing pulse, where either a X π -pulse, or Y π -pulse can bechosen as the refocusing pulse. τ delay is varied, and the experiment is performed under the same experimental conditions as inFigure 4(e), with τ π/ = 72 ns and τ π = 144 ns. Laser and MW pulses sequences (CH1, CH2, CH3) are repeated 100 × withineach half-cycle to increase the signal strength. The multi-spin representation shows the evolution of a set of pure spin statevectors on the Bloch sphere throughout the sequence. (b) Coherence time measurement for the echo sequence as in (a) withthe MW π -pulse applied along the +X (Hahn echo) or +Y axis (1-pulse CPMG). For long free precession times, the ensembleenters a mixed state, as can be seen from the convergence of the two spin signals to a common value. The solid lines are fitsto an exponential decay. Measurement time is ∼ C. Rabi oscillations
The term “
Rabi oscillations ” refers to the driven evo-lution of a two-level system that manifests as the circularmovement of the system’s state vector around the Blochsphere [5]. Successful demonstration of Rabi oscillationsmeans that we have achieved coherent control - an impor-tant step in demonstrating the viability of any quantumsystem (see also Section II). Figure 4(d) shows a detailedODMR spectrum of the | (cid:105) g ←→ |− (cid:105) g transition for B C0 . For this particular field, we have roughly aligned themagnetic field from the permanent magnet such that itsdirection is parallel to one of the three [1¯1¯1], [¯11¯1], [¯1¯11]NV − center axes, and from matching the spectrum inFigure 4(c) to theory, we can extract B = 14 . . ◦ to the best-aligned NV − axis (see Fig-ure 4(d) inset). Furthermore, the position of the perma-nent magnet was adjusted such that the | (cid:105) g ←→ |− (cid:105) g ODMR transition frequency coincides with the resonancefrequency of the PCB antenna (see Section IV C). Thisway, we subject our NV − spins to the largest B field and hence achieve the fastest Rabi oscillation frequencies [17].To observe Rabi oscillations, we set the driving fre-quency ν mw to be in resonance with the ODMR transi-tion frequency ν ODMR = 2 .
49 GHz, and vary the MWpulse length τ mw while recording the lock-in signal. Weobserve oscillations in the spin signal as a function ofpulse length, as shown in Figure 4(e), indicating coher-ent rotations of the spin around the Bloch sphere. As wehave selected only one of the 8 visible transitions in Fig-ure 4(c), we are only coherently driving NV − centers of asingle axis orientation and only from the | (cid:105) g to the |− (cid:105) g state. The oscillations can be fitted to an exponentiallydecaying sinusoid: V LI = A · sin(2 π Ω R τ mw + φ ) · e − τ mw T Rabi2 + Bτ mw + C, (3)where A is the Rabi oscillation amplitude, B is a linearterm included due to an observed increase in signal withincreasing τ mw (possibly due to heating of the sample dueat long τ mw ), C is an offset, Ω R = 2 . ± .
02 MHz is theRabi frequency, φ = − . ± .
09 is the phase-offset ( − π for ideal Rabi oscillations), and T Rabi2 = 1 . ± . μ s isthe driven coherence time of the spin [18, 19]. The T Rabi2 coherence time describes how long the | (cid:105) g ←→ |− (cid:105) g transition in the ensemble can be driven before the en-semble dephases into a mixed-state. This is due to boththe inhomogeneity of the B field over the region of thesample in focus, and the inhomogeneous broadening ofresonance frequencies over the NV − centers being mea-sured.From the Rabi oscillations, we can calibrate the exact π/
2- and π -pulse lengths as τ π/ = 72 ns and τ π = 144 ns.These pulse times will be important for the experimentsin the following section (Section V D), where we constructdynamical decoupling pulse sequences out of π/
2- and π -pulses. D. Coherence times and dynamical decoupling
In the next experiment we measure the coherence time T of the NV − centers. T is the time over which a well-defined phase relation between a quantum state and a ref-erence clock can be preserved, before noise and couplingto the environment randomize it. Thus, it is especiallyinteresting to investigate the coherence time of quantumsystems at room temperature, where the large amountof thermal energy leads to a particularly noisy environ-ment. T is also one of the key metrics for comparingdifferent quantum systems, however, as there are differ-ent definitions of T , it important to use the same metricwhen comparing different quantum systems. One suchcoherence time was already determined in Figure 4(e)and is the coherence time of the system while it is driven( T Rabi2 ). In the following experiments we look at the co-herence time during free precession of the spins usingdifferent dynamical decoupling sequences.Dynamical decoupling methods make use of refocusingpulses, as in the Hahn-echo sequence [20] [see also Fig-ure 5(a)], to refocus the phases of spins that precess atslightly different rates. Here, one differentiates betweeninhomogeneous dephasing where the transition frequen-cies of individual NV − centers are shifted due to theirlocal environments, e.g. due to static inhomogeneities inthe sample itself or in the applied B magnetic field, andhomogeneous dephasing where the transition frequenciesof all NV − centers are broadened by similar amounts,e.g. due to dynamic noise or the finite lifetime of thequantum state. Sequences consisting of refocusing pulsesare very good at refocusing static shifts in transition fre-quencies – a single refocusing pulse (as in the Hahn echo)is sufficient to decouple the quantum system from staticnoise [20]. Noise of finite frequencies is refocused as longas its frequency is much lower, or much higher than therefocusing pulse repetition frequency, which can be bestunderstood in the filter function formalism as describedin Refs. [21, 22]. In fact, changing the pulse repetition fre-quency changes the frequency spectrum the spin remainssensitive to, which allows conducting detailed investiga- tions of the noise spectrum [22–25].In Figure 5(a) we show the pulse sequence used tomeasure the Hahn echo coherence time T Hahn2 , while theBloch spheres at the bottom of the panel give an indi-cation of the spin orientations at specific points of thesequence. A first X π/ -pulse rotates the spin to the +Ydirection on the Bloch sphere. The spins are left to freelyprecess for a time τ delay , before a X π -pulse rotates themto the -Y direction. Any phase that they might have ac-cumulated with respect to the rotating frame until then(as indicated by the coloured arrows) will be unwoundin the second free precession time τ delay , before a finalX π/ -pulse rotates them to the +Z direction for read-out. We present the corresponding experimental data inFigure 5(b). Here, τ delay is increased until any phase rela-tion is randomized and the spin signal saturates, indicat-ing a completely mixed state. The spin refocusing pulsecan be applied along either the +X (Hahn echo) or +Yaxis (using IQ modulation as described in Section IV C),with the system entering into the same mixed-state ineither case as shown in Figure 5(b). We fit the datato an exponential decay and extract a coherence time of T Hahn2 = 1 . ± . μ s.Instead of a single refocusing pulse, multiple such re-focusing pulses can be applied to further extend the spincoherence time. However, performing multiple refocus-ing pulses about the +X axis leads to an accumulation ofpulse errors. Hence, refocusing pulses about the +Y axis– known as Carr-Purcell-Meiboom-Gill (CPMG) spin-echo pulse sequence [26, 27] – are more advantageous. Forthe CPMG pulse sequence shown in Figure 6(a), N CPMG is the total number of Y π -pulses, and t = N CPMG τ delay is the total free precession time of the NV − spin. TheCPMG pulse sequence acts as a bandpass filter – in-creasing the number of refocusing pulses for a fixed τ delay sharpens the filter, whereas decreasing the time τ delay be-tween refocusing pulses has the effect of shifting the cen-ter of the filter to higher frequency. The bandpass centerfrequency is given by πτ delay [22].In Figure 6(b), we plot the result of CPMG sequenceswith an increasing number of refocusing pulses N CPMG .For the same total free precession time, a larger N CPMG implies a shorter τ delay , and hence a larger center fre-quency of the CPMG filter function [28]. The normal-ized lock-in signal as a function of total free preces-sion time can be fitted to C ( t ) = A exp[( − tT CPMG2 ) n ].We plot the extracted T CPMG2 in Figure 6(c) and ob-serve a clear correlation between T CPMG2 ( N CPMG ) and N CPMG , suggesting that the noise spectral density of theNV − electron’s environment reduces towards higher fre-quencies. T CPMG2 ( N CPMG ) = B ( N CPMG ) α with α =0 . ± .
13, which is within the bounds experimentallydetermined in Ref. [28] for a CVD grown diamond witha large NV − density ( ∼ cm − ).0 FIG. 6. (a) Pulse sequences for the CPMG spin-echo se-quence, where N CPMG is number of Y π refocusing pulses.Laser and MW pulse sequences (CH1, CH2, CH3) are re-peated 100 × within each half-cycle to increase the signalstrength. (b) Examples of CPMG measurements for differ-ent N CPMG . The measurement time is ∼ T CPMG2 for all CPMG scans.
VI. CONCLUSION
We have presented a cost-effective experimental setupthat is suitable for demonstrating coherent spin controlconcepts in an undergraduate teaching laboratory en-vironment. The experiments rely on optically-detectedmagnetic resonance of NV − centers at room temperatureand require minimal optics and electronics components.Students will develop an intuitive feeling for quantumspin physics, gain first-hand experience in controllinga quantum system, and have the freedom to developunique pulse sequences and observe the results in real-time. The use of a high-density NV − diamond sampleprovides a large signal, making the measurements insen-sitive to misalignment of the optics and exposure to highambient light levels – as desirable for an undergraduatelab setup. ACKNOWLEDGMENTS
We would like to thank Jean-Philippe Tetienne for use-ful discussions, and Ye Kuang, Meilin Song, and YiwenZhang for their contributions. We acknowledge supportfrom the School of Electrical Engineering and Telecom-munications at UNSW Sydney, and the Australian Re-search Council (CE170100012). H.R.F. acknowledges thesupport of an Australian Government Research Train-ing Program Scholarship. J.J.P. is supported by anAustralian Research Council Discovery Early Career Re-search Award (DE190101397). ∗ [email protected] † [email protected][1] J. P. Dowling and G. J. Milburn, Philosophical Trans-actions of the Royal Society of London. Series A: Math-ematical, Physical and Engineering Sciences , 1655(2003).[2] M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko,J. Wrachtrup, and L. C. Hollenberg, Physics Reports , 1 (2013).[3] H. Zhang, C. Belvin, W. Li, J. Wang, J. Wainwright,R. Berg, and J. Bridger, American Journal of Physics , 225 (2018).[4] Qutools, “Quantum sensing by diamond magnetometer,” , accessed 26/03/2019.[5] T. S. Humble, H. Thapliyal, E. Munoz-Coreas, F. A. Mo-hiyaddin, and R. S. Bennink, IEEE Design & Test ,69 (2019).[6] T. D. Ladd and M. S. Carroll, Encyclopedia of ModernOptics , 467 (2018).[7] X. Zhang, H.-O. Li, K. Wang, G. Cao, M. Xiao, andG.-P. Guo, Chinese Physics B , 020305 (2018). [8] L. M. Vandersypen and I. L. Chuang, Reviews of ModernPhysics , 1037 (2005).[9] J. Clarke and F. K. Wilhelm, Nature , 1031 (2008).[10] H. H¨affner, C. F. Roos, and R. Blatt, Physics Reports , 155 (2008).[11] A. Boretti, L. Rosa, J. Blackledge, and S. Castelletto,Beilstein Journal of Nanotechnology , 2128 (2019).[12] E. Abe and K. Sasaki, Journal of Applied Physics ,161101 (2018).[13] K. Sasaki, Y. Monnai, S. Saijo, R. Fujita, H. Watanabe,J. Ishi-Hayase, K. M. Itoh, and E. Abe, Review of Sci-entific Instruments , 053904 (2016).[14] The factor of comes from the fact that we are using anoscillating, not a rotating, magnetic field.[15] J. H. Scofield, American Journal of Physics , 129(1994).[16] By convention the first pulse defines the rotation axis as+X.[17] Due to the geometry of the PCB antenna, the B fieldthat it generates is along [111] crystal direction. This ren-ders it ineffective for driving magnetic resonance transi-tions on the [111]-oriented NV − centers. However, for the [1¯1¯1], [¯11¯1], [¯1¯11]-oriented NV − centers, B is only mis-aligned from the optimal perpendicular configuration by19 . ◦ , resulting in a 94% effective magnetic resonancedrive.[18] F. Yan, S. Gustavsson, J. Bylander, X. Jin, F. Yoshihara,D. G. Cory, Y. Nakamura, T. P. Orlando, and W. D.Oliver, Nature Communications , 2337 (2013).[19] A. Laucht, R. Kalra, S. Simmons, J. P. Dehollain, J. T.Muhonen, F. A. Mohiyaddin, S. Freer, F. E. Hudson,K. M. Itoh, D. N. Jamieson, et al. , Nature Nanotechnol-ogy , 61 (2017).[20] E. L. Hahn, Physical Review , 580 (1950).[21] M. Biercuk, A. Doherty, and H. Uys, Journal of PhysicsB: Atomic, Molecular and Optical Physics , 154002(2011).[22] J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara,K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J.-S.Tsai, and W. D. Oliver, Nature Physics , 565 (2011).[23] G. A. ´Alvarez and D. Suter, Physical Review Letters ,230501 (2011).[24] J. T. Muhonen, J. P. Dehollain, A. Laucht, F. E. Hud-son, R. Kalra, T. Sekiguchi, K. M. Itoh, D. N. Jamieson,J. C. McCallum, A. S. Dzurak, and A. Morello, NatureNanotechnology , 986 (2014).[25] K. Chan, W. Huang, C. Yang, J. Hwang, B. Hensen,T. Tanttu, F. Hudson, K. M. Itoh, A. Laucht, A. Morello, et al. , Physical Review Applied , 044017 (2018).[26] H. Y. Carr and E. M. Purcell, Physical Review , 630(1954).[27] S. Meiboom and D. Gill, Review of Scientific Instruments , 688 (1958).[28] N. Bar-Gill, L. M. Pham, C. Belthangady, D. Le Sage,P. Cappellaro, J. R. Maze, M. D. Lukin, A. Yacoby, andR. Walsworth, Nature Communications , 858 (2012). APPENDIX A: LIST OF PARTS
Item Supplier Part Number Application Price (USD) Qty Total (USD)(17/12/2019)Housing
Aluminum Breadboard Thorlabs MB3045/M Base plate 199.45 1 199.45Enclosure Thorlabs XE25C7/M Enclosure for all optics 199.11 1 199.11
Optical Excitation
SM Fiber-Pigtailed Laser Diode Thorlabs LP520-SF15 Excitation laser 717.45 1 717.45Laser Diode ESD Protection Thorlabs SR9HA Laser diode protection 54.11 1 54.11Fiber Adapter Plates Thorlabs SM1FC - FC/PC Laser fiber coupling 31.38 1 31.38Kinematic Mount Thorlabs KM100T Laser mounting 70.87 1 70.8750 mm Pedestal Pillar Post Thorlabs RS2P/M Laser mounting 28.95 1 28.95Aspheric Lens Thorlabs C280TMD-A Laser collimation lens 85.49 1 85.49SM1 to M9 Lens Cell Adapter Thorlabs S1TM09 Lens mounting 24.35 1 24.35SM1 Lens Tube 1.50in Thorlabs SM1L15 Lens mounting 16.17 1 16.17Longpass 550 nm dichroic mirror Thorlabs DMLP550 Excitation/detection filtering 182.88 1 182.88Kinematic Mount Thorlabs KM100 Dichroic mirror mount 39.86 1 39.8650 mm Pedestal Pillar Post Thorlabs RS2P/M Dichroic mirror mount 28.95 1 28.95Microscope Objective Olympus MS Plan 50x/0.80NA Excitation lens 744.00 1 744.00RMS Threaded Cage Plate Thorlabs CP42/M Objective lens mount 32.78 1 32.7850 mm Pedestal Pillar Post Thorlabs RS2P/M Objective lens mount 28.95 1 28.955 mm Post Spacer Thorlabs RS5M Objective lens mount 8.17 1 8.17
Sample Mount
Imaging
Protected Silver Mirror Thorlabs PF10-03-P01 Imaging mirror 53.58 1 53.58Flip Mount Thorlabs TRF90/M Mirror mounting 88.73 1 88.7338 mm Pedestal Pillar Post Thorlabs RS1.5P4M Mirror mounting 25.21 1 25.21600 nm Longpass Filter (optional) Thorlabs FEL0600 Imaging filtering 80.62 1 80.62900 nm Shortpass filter (optional) Thorlabs FES0900 Imaging filtering 80.62 1 80.62SM1 Lens Tube 0.50in (optional) Thorlabs SM1L05 Filter mounting 12.97 2 25.94Achromatic Doublet Thorlabs AC254-125-A Imaging lens 81.16 1 81.16SM1 Lens Tube 1.50in Thorlabs SM1L15 Lens mounting 16.17 1 16.17CMOS Camera Thorlabs DCC1545M Imaging camera 387.92 1 387.92SM1 Lens Tube Spacer 3.50in Thorlabs SM1S35 Lens/camera mounting 25.53 1 25.53SM1 Cage Plate Thorlabs CP33/M Lens/camera mounting 16.89 2 33.7850 mm Pedestal Pillar Post Thorlabs RS2P/M Objective lens mount 28.95 2 57.905 mm Post Spacer Thorlabs RS5M Objective lens mount 8.17 2 16.34
Detection
Protected Silver Mirror Thorlabs PF10-03-P01 Detection mirror 53.58 2 107.16Kinematic Mount Thorlabs KM100 Mirror mounting 39.86 2 79.7250 mm Pedestal Pillar Post Thorlabs RS2P/M Mirror mounting 28.95 2 57.90600 nm Longpass Filter Thorlabs FEL0600 Detection filtering 80.62 1 80.62900 nm Shortpass filter Thorlabs FES0900 Detection filtering 80.62 1 80.62SM1 Lens Tube 0.50in Thorlabs SM1L05 Filter mounting 12.97 2 25.94Aspheric Lens Thorlabs C260TMD-B Fiber coupling lens 85.49 1 85.49SM1 to M9 Lens Cell Adapter Thorlabs S1TM09 Lens mount 24.35 1 24.35XY-Axes Translation Mount Thorlabs ST1XY-D/M Fiber alignment 517.26 1 517.2638 mm Pedestal Pillar Post Thorlabs RS1.5P4M Fiber coupler mounting 25.21 1 25.214 mm Post Spacer Thorlabs RS4M Fiber coupler mounting 7.90 1 7.90Z-Axis Translation Mount Thorlabs SM1Z Fiber alignment 205.60 1 205.602-inch Rods Thorlabs ER2 Fiber alignment 6.28 4 25.12Fiber Adapter Plates Thorlabs SM1FC - FC/PC Fiber coupling 31.38 1 31.3850 micron FC/PC Multimode Fiber Thorlabs M42L01 Detection fiber 70.87 1 70.87Si Photodetector Thorlabs DET025AFC/M Signal detection 306.00 1 306.00
Mounting
M6 Clamping Fork Thorlabs CF125C/M Mounting 11.69 9 105.21
Sample
CVD Diamond Sample Element Six 145-500-0274-01 Sample 130.00 1 130.00(e.g. SC Plate CVD (cid:104) (cid:105) ) B0 and B1 Magnetic Fields
PCB Antennas (pack of 5) Circuit Labs B1 Microwave Excitation 72.16 1 72.16Neodymium Block Magnets 10x10x5mm AMF Magnets B0 Static Magnetic Field 2.30 4 9.20
Total Optics Cost: 6780.60 Item Supplier Part Number Application Price (USD) Qty Total (USD)(17/12/2019)
USB Pulse Blaster SpinCore PBESR-PRO-250-USB Pulse Sequences 4485.00 1 4485.00Dual Phase Lock-In Ametek 5210 Lock-in detection 2000.00 1 2000.00Windows PC 2000.00 1 2000.006 GHz Microwave Source SignalCore SC800 Microwave Drive 1295.00 1 1295.00Benchtop 3-Channel PSU Newark HM7042-5.02 Microwave Drive Power 1155.00 1 1155.00RF Amplifier Mini-Circuits ZQL-2700MLNW+ Microwave Drive 304.95 1 304.95IQ Modulator Texas Instr. TRF370417EVM Microwave Drive 199.00 1 199.0012V DC Wall Adapter Thorlabs LDS12B Home-built current source 85.22 1 85.22RS232 Serial Adapter StarTech ICUSB232DB25 Lock-in detection 20.99 1 20.99BNC-BNC Coaxial Thorlabs 2249-C-48 TTL Signals 19.29 5 96.45SMA-SMA Coaxial 12-inch Thorlabs CA2912 Microwave interconnects 15.69 4 62.76SMA 50-ohm termination Mini-Circuits ANNE-50X IQ Modulator 15.95 2 31.90BNC-SMA Adapter Thorlabs T4290 IQ Modulator 14.07 2 28.14USB A-Mini B Cable Thorlabs USB-AB-72 Microwave Source 8.87 1 8.87USB A-B Cable Thorlabs USB-A-79 Pulse Blaster 8.87 1 8.87BNC-Banana Adapter Thorlabs T1452 Laser Diode ESD Protection 8.65 1 8.65Banana Patch Cable Thorlabs T13120(2) Microwave Drive Power 7.31 4 29.24
Total Electronics Cost: 11820.04 APPENDIX B: DESIGN OF THE LASER DRIVER
Schematic of the custom current source used in this experiment, broken down into the three main blocks. A . Thecircuitry supplying the current to the diode. U3 is an off-the-shelf current source integrated circuit that has theoutput current set by R3 and R4 to ∼
165 mA. As U3 requires some time to settle to a steady state current, ifwe were to modulate this current directly, we would not be able to operate at the desired bandwidth of 10 MHz.Thus we construct a current mirror using Q6; a matched pair of N-channel MOSFETs. The mirror sources 165 mAthrough the diode, unless the connection is interrupted by Q8. This allows U3 to output a constant, stable current,circumventing the switching speed problems. B . Power supplies required for the operation of the circuit. There aretwo options available for the operation of this circuit. In ‘Option 1’, an external 12 V input can be provided, whichis then regulated down to Vss by U2. In ‘Option 2’, a lab power supply can be directly connected to the circuit toprovide the power. Vss was set to -9 V as a safety feature. The case of the laser diode is at the electrical potentialof the anode and thus, this potential was set to ground. As a consequence, a negative supply voltage is required. Forthe current source that was used to obtain the results in this paper, there was a soldering error with the power supplyprovided by U2 in ‘Option 1’, and thus ‘Option 2’ was used. We have populated another PCB with ‘Option 1’ foranother teaching setup and confirmed that it functions correctly. C . Input logic and a level shifter. This block takesthe TTL input signal and level-shifts it between ground and Vss. Such voltage levels are required to correctly drivethe MOSFETs in block A , as standard TTL levels would not be able to switch Q8 due to the presence of negativesupply voltages.5 Component Description Supplier Part Price (USD) Qty Total (USD)Number (17/12/2019)
U1 LDO 3V3 Regulator Element 14 1469102 1.6 1 1.6U2 Integrated Power Supply RS Online 798-1290 19.05 1 19.05U3 Current Source RS Online 779-9615 5.58 1 5.58J1 J3 J4 BNC Connector Element 14 1169739 7.25 3 21.75J2 Barrel Jack Element 14 1854514 1.25 1 1.25Q1 PFET Element 14 1510765 0.27 1 0.27Q8 NFET Element 14 2317616 0.2 1 0.2Q6 Dual NFET Element 14 2706719 1.07 1 1.07R1 1 kΩ Resistor 0603 Element 14 2284191 0.14 1 0.14R3 16 . µ F Capacitor 1206 Element 14 2118134 0.61 2 1.22C2 C3 C7 1 µ F Capacitor 0603 Element 14 1845736 0.16 3 0.48C6 C8 C9 C10 C11 100 nF Capacitor 0603 Element 14 1709958 0.02 5 0.1C5 100 µ F Capacitor 0603 Element 14 2354734 1.57 1 1.57PCB Seeed Studio 57.86 1 57.86
Total PCB Cost: 113.33 -200 0 200 4000.51.52.5 -10-8-6-4-202-2 0 2 4 6 8012 -10-50Laser off Laser on(a) (b) -200 0 200 4000.51.52.5 -8-6-4-2020 50 100012 -10-500.01.02.03.0 0.01.02.03.0-200 0 200 4000.51.52.5 -10-8-6-4-202-2 0 2 4 6 8012 -10-50Laser off Laser on(a) (b) -200 0 200 4000.51.52.5 -8-6-4-2020 50 100012 -10-500.01.02.03.0 0.01.02.03.0