Delay and polarization routing of single photons
Julian Maisch, Hüseyin Vural, Michael Jetter, Peter Michler, Ilja Gerhardt, Simone Luca Portalupi
DDelay and polarization routing of single photons
Julian Maisch , ∗ H¨useyin Vural , Michael Jetter , Peter Michler , Ilja Gerhardt , and Simone Luca Portalupi Institut f¨ur Halbleiteroptik und Funktionelle Grenzfl¨achen (IHFG),Center for Integrated Quantum Science and Technology (IQ ST ) and SCoPE,University of Stuttgart, Allmandring 3, D-70569 Stuttgart, Germany and
3. Institute of Physics, Center for Integrated Quantum Science and Technology (IQ ST ),University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany The full control of single photons is important in quantum information and quantum networking.A convenient storage device for photons is the key to memory assisted quantum communication andcomputing. While even a simple optical fiber can act as a convenient and reliable storage device, itsstorage time is tightly fixed and cannot be adapted. Therefore, the photon storage should ideallybe actively controllable by external means, such as magnetic or electric control fields. In orderto multiplex several photons, an active routing would also be desirable. Here we show that singlephotons of a semiconductor quantum dot can be deliberately delayed by an atomic vapor. Also,the output path can be selected, depending on an external magnetic field. By selecting the inputpolarization of the photons and by aligning the external magnetic field of the hot atomic vapor,the delay-based storage can be fine tuned to a deliberate value. With an overall delay of 25 ns, weare able to fine tune by more than 600 ps. Depending on the input polarization, the photons arerouted into different output ports. The experimental data is fully resembled by a theoretical model,which describes the group velocity delay under consideration of spectral diffusion and considersthe complex refractive index of the atomic vapor. The present results enable the use of an atomicvapor as a wavelength selective delay and allows for routing the single photons according to theirpolarization and an external magnetic field.
I. INTRODUCTION
Single photons are an essential ingredient of modernquantum information processing. Encoding informationinto single photons will result in highly secure data trans-fer which becomes particularly appealing for the imple-mentation of quantum cryptography and communica-tion [1]. To be beneficial in the up-scaling of the ex-perimental complexity, their generation is ideally real-ized in a deterministic or turnstile way, such that a sin-gle photon can be generated on demand. This formsthe key advantage of single emitter based single pho-ton sources against so-called parametric down-conversionsources. Typically on-demand single photon sources orig-inate from single atoms [2] and ions, over molecules [3] todefect centers [4] and quantum dots [5]. Since quantumdots (QDs) are based on semiconductor technology, theyhold the promise to be integrated onto chip-scale devices.Furthermore their option to generate polarization entan-gled photons [6, 7] opens the potential for a variety ofquantum information schemes, which are enabled withthis quantum phenomenon.Current state-of-the-art QDs exhibit high brightness,high indistinguishability [8–10] and entanglement fi-delity [11]. Quantum dots therefore represent a veryappealing source of non-classical light. On the otherhand, in many quantum applications, such as quantumrepeaters, the implementation of a deterministic quan-tum memory is beneficial. At present, the relativelyshort coherence times of the QD’s spin may limit their ∗ [email protected] performance as storage media. In contrast, atomic sys-tems with their high coherence and long storage timescould provide this option [12]. Still, the implementationof a full storage experiment is a challenging task. Forinstance, the intensity mismatch between single photonsand the required high power control fields complicatesthe experimental realization. Another limiting factor isthe bandwidth mismatch, when e.g. broad photons haveto be stored in a spectrally narrow medium. An inter-mediate step towards the on-demand realization is theimplementation of an optical delay line within an atomicmedium. First results with laser pulses [13–15] prove thatan atomic vapor has a large application potential [16].Such experiments have set the basis for recent exper-iments where single photons were slowed down withinalkali vapors [17–21]. These experiments show impress-ingly the compatibility of single photons from quantumdots with their atomic counterparts. Still, photonic rout-ing, or photon multiplexing [22] was not shown in thesepapers.Here we report on the experimental combination ofimplementing a fine-tunable delay and simultaneous pho-tonic routing in a hot atomic cesium vapor. The experi-ments are conducted with a semiconductor quantum dotas an on-demand source of single photons. The delay andthe routing is implemented by a 250 mm long Cs-vaporcell in a externally controllable magnetic field. Depend-ing on the external magnetic field, the two polarizationcomponents of the light are affected differently. This fea-ture can be deliberately controlled and fine-adjusted bythe external magnetic field. a r X i v : . [ qu a n t - ph ] M a y II. THEORY
The refractive index in a hot atomic vapor is tied to thestrong absorption lines and the dispersion in the medium.This well-know phenomenon is usually represented by adivision into a real and an imaginary part of the refractiveindex – the Kramers-Kronig relation. The index can bedivided as n = n (cid:48) + in (cid:48)(cid:48) . With the electric susceptibility, χ , this is approximately equivalent to n = 1+2 πχ , where χ is represented as χ = N e / mω ( ω − ω ) − iγ . (1)Here, N represents the number of involved atoms, e isthe electron charge, and ω represents the transition and ω the laser frequency. γ represents the radiative lifetimeof the excited state. Therefore, in other words, the re-fractive index is represented by the two components n (cid:48) = 1 + πN e mω γ ω − ω ) γ ( ω o − ω ) + γ (2) n (cid:48)(cid:48) = πN e mω γ γ ( ω − ω ) + γ . (3)The group velocity inside a medium of group index isknown to be given as n g = n (cid:48) + ωdn (cid:48) /dω . When thegroup index is larger than unity “slow light” can be ob-served [17, 18, 21], while for an index below unity “fastlight” is expected [23, 24].The Zeeman-effect is responsible for a spectral splitof the atomic lines under the influence of a longitudi-nal magnetic field. This naturally influences not onlythe absorption but also the dispersive components of therefractive index. Both of the two split dispersion com-ponents act differently on circular polarized light. Thisholds consequently also for linearly polarized light, whichrepresents as a linear-combination of two circular fields.In summary, this leads to an effective rotation of lightwhich is based on the Faraday effect [25]. This has beenused in Faraday filters and the symmetry breaking allowsto utilize this effect for optical isolation on or close to theatomic resonance [26].Both schemes analyze the input of linear polarized lightand rely on the effective rotation of the linear componentby the atomic medium. A linear analyzer behind a vaporcell, which is orthogonally oriented to the input polariza-tion to the vapor cell, can be passed and the net rotationis quantified. Similarly, the effect allows for laser lock-ing by the individual analysis of the circular polarizationcomponents of the beam. This is known as a dichroicatomic vapor laser lock (DAVLL, Ref. [27, 28]). Here,the circular components are analyzed behind the cell bythe combination of a quarter-waveplate and a polariz-ing beam splitter. Each of the two circular componentsshows a different spectral shift and the difference of bothsignals forms dispersive lines for each transition. The zero crossing is usually a reliable lock-point and is usedfor laser locking [29].Naturally, also the group velocity of the light is af-fected by the dispersion in the atomic medium. In thecase of a monochromatic input field, it can be determinedby calculating the effective refractive index of the dif-ferent atomic transitions and and calculate the groupvelocity based on these. Under broadband, i.e. non-monochromatic, illumination different spectral compo-nents are affected differently. The resulting delay is rep-resented by an integration of the individual delays overthe entire spectrum and is generally more complex thanin the monochromatic case [30]. When this is mathemat-ically estimated it becomes clear that a) a light pulse isdelayed and smears out more the longer the delay is, andb) that characteristic fingerprints can be observed andthe pulse shape is affected in a non-trivial way [21].The above description of slow light is not limited ona single frequency light input. In addition, when a mag-netic field is applied to the hot atomic vapor, both cir-cular components (even when the fields are of the samefrequency) are influenced differently. Therefore, in thefollowing both polarization components are analyzed. III. EXPERIMENT
The experimental configuration is shown in Figure 1.The input light is linearly polarized and the light is ana-lyzed for its circular components with the aid of a quarterwave plate and a polarizing beam splitter. For the initialalignment a laser and commercially photo diodes withvariable gain are used, while the atomic cell is at a lowtemperature, or the laser is several tens of GHz spectrallydetuned from the atomic resonance. The light is suppliedto the experiment with a single mode fiber.The atomic vapor cell for these experiments is made ofborosilicate glass and has a length of 250 mm. The cellis heated by four round copper blocks which are approx.equally spaced along the length of the cell. The two mostouter copper blocks heat the cell windows and preventcondensation of the atomic cesium on them. The coldestspot of the cell was aligned with the filling stem of thecell by a piece of aluminum foil which touches the colderparts of the coil from the inside.When the atomic vapor is heated, an atomic trans-mission spectrum with Doppler broadened lines is ob-served. The cesium D -line shows the well-characterizedground state splitting of 9.192 GHz, plus the excited statesplitting of 1.2 GHz. Since the latter is larger than theDoppler broadening of the vapor –at least under ambientconditions– usually four lines are observed. At highertemperatures, the excited state transitions merge andonly two dominant absorption features are observed. Be-tween them, the transmission window shows the typi-cal 1 /δν detuning frequency dependence and a smallwindow is kept open, which is used to perform the ex-periments below. This is also the window where slow QDs APDsPulse Laser TimeTaggerPBS λ /4 startstoptrig CesiumBmagnetic fieldPolPBS σ + σ -fiber Figure 1. Experimental setup for time-correlated single photon counting (TCSPC). The quantum dot (QD) is resonantlyexcited. Through the polarizer (Pol) the single photons enter the cesium vapor cell linearly polarized. A variable magneticfield can be applied parallel or anti-parallel to the propagation direction. Behind the vapor cell the quarter wave plate ( λ/ light can be efficiently observed, since there the effectivegroup index dn/dω is approx. twice as large as besidesthe atomic transitions [31].It is possible to apply a magnetic field to the cell, suchthat the Zeeman components are split. This is realizedwith a long solenoid of enameled copper wire (0.8 mm ∅ ).The solenoid is thermally isolated with Teflon supportsfrom the cell heater. After some hours of heating a stabletemperature is reached. It is worth mentioning that alsothe current through the coil also heats the system, whichin turn affects the temperature during the application ofa magnetic field. This fact becomes relevant when themagnetic field is changed.The single photon source used here is a strain-tunableIn(Ga)As/GaAs quantum dot which is grown by metal-organic vapor-phase epitaxy [32]. The light-extractionis facilitated by two distributed Bragg reflector (DBR)layers. A pulsed laser with a repetition rate of approx.15 MHz (by pulse picking a standard 80 MHz Ti:Sapphirelaser) excites the quantum dot resonantly, while a weak,non-resonant second laser stabilizes the transition. Si-multaneously, it prepares a charged exciton transition byexciting charge carriers which initially charge the QD.For single photon detection two standard single pho-ton counting modules were utilized (Excelitas SPCM-AQRH), in combination with time-tagging electronics(Swabian Instruments “Time Tagger 20”) to evaluate thephoton statistics.First, we investigate the vapor spectroscopically withan applied magnetic field. Figure 2a shows the setupwhere the light enters the vapor horizontally polarized.The light polarization is altered due to the Faraday ef-fect and is detected by a pair of photodiodes behind apolarizing beam splitter. The resulting polarization de-pendent transmission is exemplarily shown for T=80 ◦ Cand B=8 mT in Figure 2b. The spectra of both compo-nents show oscillating modulations besides the well knowabsorption profile. The transmission oscillates betweenzero and the maximal transmission, dictated by the over- all vapor absorption. The observed frequency dependentpolarization rotation is a consequence of a phase differ-ence between the circular polarization components of thelight, due to the circular birefringence induced by themagnetic field. The same effect causes a polarizationdependent delay in measurements with pulsed light asobserved with laser light on Ref. [14, 15].Here, we perform an experiment with single photonsunder resonant pulsed excitation. Figure 3a shows themeasured second order correlation function of the emis-sion. The vanishing central peak ( g (2) (0)=0.03) clearlyproves the single-photon nature. Figure 3b shows thespectrum of the QD. A nearly Gaussian profile with3 GHz width is observed. This well-known shape can beattributed to the presence of spectral diffusion. As com-parison, the Cs absorption at 130 ◦ C is depicted. Thewidth of the QD emission is on the same scale as thewidth of the transmission window.Due to dispersion in the vapor, the group velocity ofphotons inside the medium is reduced. Therefore, slowlight is observed. In absence of a magnetic field, the de-lay through the heated atomic vapor amounts to approx.25 ns. We like to note that this delay was similarly ob-served in our previous work [21].When a magnetic field is applied, it influences thetwo circular components of the propagating light differ-ently. This results in different refractive indices and con-sequently in different group velocities for both compo-nents. The setup for the TCSPC measurements is shownin Figure 1. The QD is excited by resonant π -pulse.A polarizer before the vapor cell ensures that the pho-tons enter horizontally polarized. Afterwards a λ /4-plateand a polarizing beam splitter project the both circularcomponents ( σ + and σ -) onto two separate APDs. Therecorded signals of slow light under different magneticfields are shown in Figure 4a-c. While both signals over-lap for zero magnetic field (b), one clearly observes thealtered delay if a magnetic field of B =+16 mT is ap-plied (a). Reversing the orientation of the magnetic field ReferenceScanning Laser CesiumBMagnetic FieldPol a Detector 1Detector 2 b ( → pol)( ↑ pol) c TheoryDataPBSBS → polarization ↑ polarization Figure 2. (a) Setup for measuring the Cs-D absorption spectra of the polarization components. The polarizer (Pol) ensuresthat the light enters the vapor cell linearly polarized. The polarizing beamsplitter (PBS) separates the orthogonal polarizationcomponents at the two detectors. (b) and (c) Measured (dotted lines) and calculated (solid lines) spectra for the Cs-D absorption in a 250 mm long vapor cell at temperature of 80 ◦ C and a longitudinal magnetic field of 8 mT. The two panels showthe separated polarization components: (b) horizontal and (c) vertical. (i.e. B =-16 mT is applied (c)), simultaneously inversesthe delay of the two polarization components. Due tothe complex absorption spectrum, the lines are differ-ently affected. The modulations on top of the photonwave packages are due to the vapor’s dispersion [21]. Inthe experimental signals they occur blurred. The reasonare thermal fluctuations which are induced by the coilaround the vapor cell. The current through the windingsproduces additional heat which affects the vapor tem-perature when the maximum current of ± n ( ν ) and α ( ν )). With that it is possible to calculate the spectrumafter propagation through the vapor of length Lχ in( ν ) → χ out( ν ) = χ in( ν ) · e in c kL (4)with n c = n ( ν ) + i k α ( ν ) . (5)An inverse Fourier transformation then provides the tem-poral form of the propagated photons. This procedure isrepeatedly performed for an ensemble of photons whereeach one is assumed to be Fourier limited with a cer-tain carrier frequency. This carrier frequency is drawnfrom a random Gaussian distribution which is chosen ac-cording to the measurement result of the high-resolutionspectrum (Figure 3 b).In the theoretical curves, oscillations superimposed tothe exponentially decaying profile are observed. 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