Mode expansion and Bragg filtering enable a high-fidelity fiber-based photon-pair source
aa r X i v : . [ qu a n t - ph ] O c t Mode expansion and Bragg filtering fora high-fidelity fiber-based photon-pairsource
Alexander Ling*, Jun Chen, Jingyun Fan and Alan Migdall
National Institute of Standards and Technology, Gaithersburg, MD 20899Joint Quantum Institute, University of Maryland, College Park, MD [email protected]
Abstract:
We report the development of a fiber-based single-spatial-modesource of photon-pairs where the efficiency of extracting photon-pairs isimproved over a previous source [18] through the use of fiber-end expansionand Bragg filters. This improvement in efficiency enabled a spectrally brightand pure photon-pair source having a small second-order correlation func-tion (0.03) and a raw spectral brightness of 44,700 pairs s − nm − mW − .The source can be configured to generate entangled photon-pairs, character-ized via optimal and minimal quantum state tomography, to have a fidelityof 97% and tangle of 92%, without subtracting any background. OCIS codes: (270.4180) Multiphoton processes; (190.4370) Nonlinear optics, fibers;(190.4380) Nonlinear optics, four-wave mixing
References and links
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Fig. 1. (Color online) Layout of first experiment for pumping a PCF and collecting photon-pairs. Photon-pairs are detected via a start-stop coincidence circuit. Reflection Bragg grat-ings separate signal and idler from the pump. Using two gratings per arm suppresses thepump light by up to 180 dB.
1. Introduction
The contemporary workhorse method for obtaining photon-pairs has been Spontaneous Para-metric Down Conversion (SPDC) [1] in nonlinear crystals. Typical SPDC sources employ bulkcrystals whose output is coupled into single-mode fibers [2, 3]. However, because SPDC emis-sion from bulk crystals is inherently spatially multi-mode, only a fraction of the two-photonlight can be collected into a single-mode fiber. This is one reason that has prompted numerousstudies on SPDC inside waveguides [4, 5, 6, 7, 8], as the overlap of the total emitted light witha single spatial mode can be much greater.Another approach, which is the subject of this paper, is to generate photon-pairs via Sponta-neous Four-Wave Mixing (SFWM) inside optical fibers [9, 10, 11, 12, 13, 14, 15]. Of particularinterest is SFWM inside of a solid-core photonic-crystal fiber [16] (PCF), which has spatialmode sizes typically an order of magnitude smaller than in conventional fibers, resulting inmuch higher nonlinearity. Combined with appropriate phase-matching conditions, SFWM inPCFs has enabled very bright polarization-entangled photon-pair sources (even after aggres-sive spectral filtering) operating at room temperature [17]. However, the PCF source still hasoutstanding issues. Most significantly, the performance of PCF sources suffer from low extrac-tion efficiency; losses are typically high when the pairs are to be prepared into a well-definedbandwidth with a useful single spatial-mode.In this paper we report a novel method of improving the extraction efficiency, comparedto earlier implementations of PCF sources [18, 19]. This was enabled by incorporating novel(and simple-to-use) elements - end-tapered PCFs, high-efficiency reflection Bragg gratings andhigh-transmission band-pass filters. Our implementation has enabled us to incorporate a highercount rate with higher purity as compared to other single-mode photon-pair SFWM sources[18, 19]. The photon-pair purity of the source, determined using the second order correlationfunction (g ( ) ( ) ), was measured to be as small as 0.007. When the source is used to generatepolarization-entangled photon-pairs, the fidelity (to a Bell state) and tangle are measured to be97% and 92%, respectively. Indistinguishable photons have also been heralded by detection oftheir twins, which exhibit a high level of indistinguishability via the demonstration of a 82%raw visibility Hong-Ou-Mandel interference dip.
2. Photon-pair purity
As the basic theory of SFWM inside fibers has been well described previously [21], we beginby describing our experimental parameters. able 1. Extraction efficiencies for different PCF sources. Where possible we have pro-vided the experimental uncertainties (1 standard deviation). The values for h fiber is takenby assuming 4% reflection loss at an uncoated glass surface. Efficiency (%)Our source Source: [18] Source: [20]spectral selection method Bragg Grating Monochromator Etalon Filtersignal idler signal idler signal idler h fiber (calc.) 96 96 96 96 N.A. h lens (meas.) 98 ± ± h spectral (meas. & calc.) 28 ± ± h coupling (meas.) 50 ± ± h signal , h idler ± . ± . h pair = h signal × h idler . ± . h det ± . ± . . ± . . ± . . ± .
03 0.21 2.8
In our photon-counting experiments (Fig. 1), we work with PCFs engineered to be polarizationmaintaining along two principal axes. To maximize the nonlinear gain, the pump polarizationis aligned with the axis which exhibits higher nonlinearity; this configuration also enables thegeneration of co-polarized photon-pairs.The PCF we use has a length of one meter and a nominal zero-dispersion wavelength of745 ± ≈ m m, but the fiber structure at the ends was collapsed over a length of 50 m m to yield a 15 m mmode resulting in a smaller divergence (NA ≈ .
3, from manufacturer’s datasheet) compared tothe non-tapered PCF (NA ≈ . . ± .
06 nm, which is slightly blue of the zero-dispersion wave-length [22, 19]. This improves photon-pair purity without much loss in the pair production rateby avoiding the peak of the Raman Scattering.The pump is a pulsed Ti:Sapphire laser (repetition rate of 76 MHz, and pulse duration of8 ps). Phase matching results in the peak of the signal and idler wavelengths being emitted at690.4 nm and 801.2 nm respectively. After spectral filtering, photons are collected into single-mode fibers and detected by Si avalanche photo-diodes (APDs). Electronic signals from thedetectors are sent to a start-stop data acquisition system for coincidence detection (5 ns timewindow), with the signal photons providing the start trigger.The ends of the PCF are not anti-reflection coated resulting in a calculated emission effi-ciency of h fiber = h lens = ± ≈ ≈
90 dB, giving a combinedsuppression of 180 dB from the two gratings in series. Typical pump power is ≈ ± h grating , is estimated to be 80%. Usingtwo gratings in reflectance leads to a combined efficiency of h grating =
64% over that FWHM.Light transmitted through the grating suffers ≈
10% scattering loss.However, there is an additional loss mechanism due to the finite bandwidth of the pump beingcomparable to the filter bandwidths. From the combination of pump and filter bandwidths, wecalculate the signal photons to have a spectral width of ≈ .
39 nm. Similarly the bandwidth forthe idler photons is ≈ .
45 nm. Using the nominal filter bandwidth, the overall spectral selectionefficiency, h spectral , for the signal photons is . . × h grating ≈ . × . . × h grating ≈
38% (which suffer the additional scattering loss due to havingto traverse the signal grating).The single spatial-mode is defined by the single-mode collection fibers. Because of a lenscommon to the signal and idler paths, the signal and idler coupling efficiencies, h coupling , couldnot be optimized independently. Given this tradeoff we matched the signal and idler efficien-cies at 50 ± h signal = h coupling h spectral h lens h fiber = ± .
6% , whereas for idler photons h idler = h coupling h spectral h lens h fiber = ± . h pair = h signal h idler ≈ . h det , of 56 ± .
6% at 690.4nm and 43 ± .
4% at 801.2 nm. Thus, taking into account the above values for h det , the singlephoton detection efficiency for signal photons is 7 . ± .
3% and for idler photons is 7 . ± . .
57 with a statisticaluncertainty of ± . /A signalidler50:50 1 23 (2) g (0) C/A g (0) (2) source [15]source [22]
10 10
10 10 10 10 10
3 6
Spectral Brightness(pairs/s/nm/mW)Detected Pair Rate(pairs/s) 10 (a) (b)
10 10 10 10
10 10 10 10
2 3 4 5
2 4 5
10 10 10 −1 −2 −3 −1 −2 −3
10 10 10
Fig. 2. (Color online) Two measures of photon-pair purity: the coincidence-to-accidentalsratio (C/A) and g ( ) ( ) . (a) Photon-pair purity dependence on the detected pair rate. (b) g ( ) ( ) versus raw spectral brightness. The inset indicates the detection arrangement forobtaining g ( ) ( ) . The signal photon acts as a herald, while the idler photons are sent intoa polarization neutral 50:50 beamsplitter. The rate of three-fold and two-fold coincidencesdetermine the value of g ( ) ( ) . In both (a) and (b) the x-axis was obtained by varying pumppower, with higher power yielding higher pair rates and higher spectral brightness. Putting all the efficiencies together, we find that with our single-mode pair source, we de-tect ≈ Higher pair detection efficiency together with a narrower selected bandwidth enables a highpurity photon-pair source. The photon-pair purity is important, as it determines the backgroundcaused by erroneously identified pairs, thus limiting the number of useful pairs for experiments.This purity can be estimated using either the coincidence-to-accidentals ratio (C/A), or fromthe second-order correlation function g ( ) ( ) [28]. C/A is commonly used [14, 15] because theaccidentals rate is a direct measure of the background level. The C/A value can be obtaineddirectly from two-fold coincidence measurement setups such as the one depicted in Fig. 1.To determine C/A, it is necessary to estimate the rate of accidental coincidences. To a firstapproximation, the rate of coincidences between photons from different pump pulses is a goodestimate of the accidentals rate. Our start-stop acquisition system lets us monitor coincidenceand accidental counts simultaneously. The observed C/A taken as the pump power (and detectedpair rate) was varied for our PCF is shown in Fig. 2(a).The second-order correlation function is a direct measure of the presence of multiple photons(per pulse) in the signal and idler channels. When there is only one pair per pulse, g ( ) ( ) = g ( ) ( ) of classical coherent light sources [28]. Thuswe would expect that the g ( ) ( ) values for our source would lie somewhere between 0 and 1,when operated with low pump power.In our g ( ) ( ) measurement scheme (inset of Fig. 2(b)), the idler photons are incident on a50:50 fiber beamsplitter whose output ports are sent to APDs. The detector in the signal armacts as the herald for a three-fold coincidence. Following a simple model described in [29], thecorrelation function is g ( ) ( ) = C C ( C + C ) , (1)where the three-fold coincidence rate is C , the rate of signal photons is C , and the two-fold rate between signal and idler detectors are C and C , The three-fold coincidences weredetected with an electronic circuit based on field programmable gate array (FPGA) technology[30]. The measured correlation values (Fig. 2) are much less than 1, signifying the nonclassicalnature of the emitted light.Figure 2 (a) links photon-pair purity with the detected pair rate. From the figure, a detectionrate of 45 pairs s − ( ≈ .
05 mW) has g ( ) ( ) = . ± . → ¥ forno background accidentals). When pump power is increased to 0.5 mW, the detected pair rate is3,800 pairs s − , g ( ) ( ) = . ± .
001 and C/A=100. For comparison, we consider the lowestnoise photon-pair source we found in the literature (based on SPDC [29]). This source exhibitsa g ( ) ( ) of 0.0014 ± . − and bandwidth of 6.9 nm. Althoughreference [29] does not provide the observed pair rate, this value may be inferred from the datathat was published in the paper. To compare pair rates between sources, we normalize to thepump power and collection bandwidth and determine the raw spectral brightness of our sourceto be 44,700 pairs (s nm mW) − at 0.5 mW of pump power (Fig. 2(b)). Selected points fromFig. 2(b) are presented in Table 2.
3. Polarization-entangled photon-pairs
Here, we characterize a polarization-entangled pair source based on an end-tapered PCF. Thisis done by using a coherent superposition of | HH i and | VV i , where | HH i and | VV i representthe horizontal and vertical polarization states of photon-pairs. Such a superposition may begenerated by placing the PCF in a Sagnac loop as reported in [17, 19] (Fig. 3).To generate the orthogonal polarization states, only one principal axis of the PCF is pumpedfrom both ends. The axis at one end was aligned to match with the H output of a polarizingbeam splitter (PBS). The PCF was twisted so that the axis orientation at the other end is matchedwith the V output of the PBS. The extinction ratio of a PCF-based Sagnac loop is better than Table 2. Selected data points from Fig. 2(b) for comparing g ( ) ( ) values between differ-ent sources. Increasing the pump repetition rate, but keeping peak pulse power constant,it should be possible to increase the pair production rate while maintaining the level of g ( ) ( ) . g ( ) ( ) Detected Rate Bandwidth Spectral Brightness(pairs s − ) (nm) (pairs s − nm − mW − )Our Source 0 . ± .
005 45 0.17 5,3000 . ± .
001 3,800 0.17 44,700Source [18] 0 . ± .
002 350 0.9 7,800Source [29] 0 . ± . pump l/4 l/2 PBS
Fiber with twist BG signal PBS BP idler
PBSBP l/4 l/2l/2 l/4
Fig. 3. (Color online) Schematic of the polarization-entangled photon-pair source based ona 90 o twist of the photonic-crystal fiber. The PCF is pumped in both directions. A singleBragg grating (BG) selects for each of the signal and idler; to suppress residual pumplight highly transmissive ( > l ) and half-wave ( l ) plates together witha polarizing beam splitter (PBS). ≈ | HH i and | VV i , producing a polarization-entangled photon-pair state. Using only a single Bragggrating for each wavelength, we are able to separate the desired signal and idler photons fromthe rest of the light output. Sufficient suppression of pump light was achieved with the help ofan additional bandpass filter. These filters are centered on 800 nm (FWHM ≈
12 nm) and 692nm (FWHM ≈
40 nm) respectively, both having a measured transmission efficiency of 99%and a box-like spectral selection profile.The polarization-entangled state can be completely characterized by quantum state tomog-raphy. We used a tomographic technique that is known to be minimal and optimal [31]. Thekey point of this technique is that the polarization state of light is described by a Stokes vectorwhich has only three independent variables [32, 33]. Such a Stokes vector can be illustratedon a Poincare sphere (Fig. 4(a)). The direction and magnitude of any Stokes vector is com-pletely determined by its overlap with four reference vectors in the sphere. In contrast, standardpolarimetry requires six overlap measurements [34]. It was further shown that when these refer-ence vectors define a tetrahedron in the Poincare sphere, the characterization rate is optimized[31]. Hence, characterization of single photon polarization states requires only 4 projectivemeasurements [35]. This is of particular importance when considering N-photon states, wherethe number of projective measurements grows as 4 N [36], in contrast to standard polarimetrythat grows as 6 N .To characterize our photon-pair state, we needed to monitor 16 separate two-fold coinci-dences. This was done by projecting the signal photons sequentially onto the 4 reference polar-izations states; the reference states were prepared by rotating the half-wave and quarter-wave S S S HH HV VH VVHH HV VH VV - - unknown Stokesvector(a) (b) Fig. 4. (Color online) (a) Illustrates the concept of minimal and optimal tomography for anunknown Stokes vector. (b) A graphical representation of the density matrix obtained usingminimal and optimal quantum state tomography. The real part of the matrix is on the left;the imaginary part is the right. The magnitude of the components of the imaginary part areless than 0.013. The fidelity to the F − Bell state is 97 ± plates (Fig. 3) to the angles described in [33]. For each projection state of the signal, the idlerphotons are also projected onto the same four reference states. In this way, we obtain the 16combinations of coincidences that are sufficient to obtain a photon-pair Stokes vector that canbe converted into a density matrix [36].The source is typically operated at room temperature with a pump power of 1 mW (be-fore the PBS), and the detected pair rate is ≈ ,
800 s − . The detected rate is lower than witha single pump direction setup because the spatial mode shapes from the two fiber ends areslightly different, causing additional loss in coupling into single-mode fibers that define theuseful spatial mode as well as transmit light to the APDs. The density matrix of our photon-pair state (at 1 mW of pump power and without correcting for accidentals) is reconstructed andshown in Fig. 4(b). The fidelity of this density matrix to the maximally entangled Bell state, F − = √ ( | HH i − | VV i ) , is 97 ±
1% (error propagation assumes a Poissonian noise model andstandard error is used). The tangle is one method of quantifying the degree of entanglement,and from our measured density matrix the tangle is found to be 92 ±
4. Heralded indistinguishable single photons
Another possible use of the end-tapered PCF is as a source of heralded indistinguishable singlephotons. We note that a single PCF that is pumped bi-directionally acts as two sources of her-alded single photons (similar to some SPDC experiments where a nonlinear crystal is pumpedin two directions [37]). When combined with the spectral filtering described in previous sec-tions, the idler (and signal) photons generated from either end of a PCF are effectively indis-tinguishable. We demonstrate this by performing the classic Hong-Ou-Mandel (HOM) photoninterference measurement [38].This experiment (Fig. 5(a)) is a modification of the setup used to generate the polarization-entangled pairs where two pairs of photons are collected, one pair from each output of thePCF. Using the FPGA-based counting system, the overall rate of four-fold coincidences wasmonitored. To act as heralds for their respective idler partner, the signal photons were split offvia a PBS. The idler photons were also sent through a PBS to identify their polarization. Idlerphotons leaving from the V-polarized port of the Sagnac loop were rotated with a half-waveplate to match the polarization of the photons leaving from the H port. The photons are theninterfered on a 50:50 beamsplitter. For a well defined spatial mode and maximal spatial overlapof idler photons at the 50:50 beamsplitter, we used a single-mode fiber between the grating −as heraldssignal photons act l pump + + PCFPBSPBS50:50 retroreflector BG HOM apparatusfor idler photons single−mode fiber PBS (a) l/2 (b) after accidentalscorrectionvisibility = 100 8%visibility = 82 6% − f o l d c o i n c i den c e s i n s
34 35 37
Fig. 5. (Color online) (a) Scheme for measurement of the Hong-Ou-Mandel Interferencedip. The signal photons act as heralds for the idler photons. For interference to take place,the idler photons are set to H polarization. (b) The observed HOM dip at ≈ and the first PBS in the Hong-Ou-Mandel setup. The degree of temporal overlap between theidler wavepackets was controlled by moving a retroreflector to adjust the path delay. The rateof four-fold coincidences is recorded against the position of this retroreflector.The main source of noise in this measurement is multiple pair generation from a single pumppulse direction causing a background that reduces the visibility of the HOM interference. Thebackground rate can be determined by sequentially blocking each input port of the 50:50 beam-splitter, and adding up the remaining four-fold coincidences, and is found to be ≈ .
005 s − . At1 mW of pump power ( g ( ) ( ) ≈ .
08 and C/A ≈ ≈ .
03 s − . These should be compared against the state-of-the art in four-fold coincidencegeneration via SPDC (0 .
28 s − [39]) or SFWM ( ≈ . − [40]). It would be very interestingto combine the SFWM design techniques in [40] with end-tapered PCFs to obtain even brightersources of four-fold coincidences.When the idler photon wavepackets had maximal spatial overlap, a dip was obtained in theraw four-fold coincidence rate with a visibility of 82 ±
5. Conclusion