Polarization entanglement by time-reversed Hong-Ou-Mandel interference
Yuanyuan Chen, Sebastian Ecker, Sören Wengerowsky, Lukas Bulla, Siddarth Koduru Joshi, Fabian Steinlechner, Rupert Ursin
aa r X i v : . [ qu a n t - ph ] A ug Polarization entanglement by time-reversed Hong-Ou-Mandel interference
Yuanyuan Chen,
1, 2, 3, ∗ Sebastian Ecker,
1, 2
S¨oren Wengerowsky,
Lukas Bulla,
1, 2
Siddarth Koduru Joshi,
1, 2, †
Fabian Steinlechner, and Rupert Ursin
1, 2, ‡ Institute for Quantum Optics and Quantum Information - Vienna (IQOQI),Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria. Vienna Center for Quantum Science and Technology (VCQ), Vienna, Austria State Key Laboratory for Novel Software Technology,Nanjing University, Xianlin Avenue 163, Nanjing 210046, China.
Sources of entanglement are an enabling resource in quantum technology, and pushing the limits of generationrate and quality of entanglement is a necessary pre-requisite towards practical applications. Here, we presentan ultra-bright source of polarization-entangled photon pairs based on time-reversed Hong-Ou-Mandel interfer-ence. By superimposing four pair-creation possibilities on a polarization beam splitter, pairs of identical photonsare separated into two spatial modes without the usual requirement for wavelength distinguishability or non-collinear emission angles. Our source yields high-fidelity polarization entanglement and high pair-generationrates without any requirement for active interferometric stabilization, which makes it an ideal candidate for avariety of applications, in particular those requiring indistinguishable photons.
Introduction.
Quantum entanglement is an enabling re-source for quantum information processing (QIP) and an effi-cient source of entangled photons can now be considered anabsolute necessity in the quantum mechanic’s toolkit. En-tangled photons can be generated using a variety of techno-logical approaches [1], with spontaneous parametric down-conversion (SPDC) in nonlinear materials representing thepresent-day gold standard with respect to fiber coupling ef-ficiency [2, 3], entangled photon pair rates [4], and entangle-ment fidelity [5]. In the SPDC process, photons from a strongpump laser (p) spontaneously decay into two daughter pho-tons, commonly referred to as signal (s) and idler (i), whichcan be tailored to exhibit entanglement in various photonic de-grees of freedom. SPDC offers a wide range of possibilitiesto generate polarization entanglement [6–12], with two widelyused source configurations being the crossed-crystal scheme,in which two parametric down-converters, rotated by ○ withrespect to each other, are placed in sequence and pumped witha diagonally polarized pump laser [7], and the Sagnac scheme,where a single down-converter is bi-directionally pumped in-side a polarization Sagnac interferometer (PSI) [8, 10]. Theseschemes owe their popularity to the fact that no active inter-ferometric stabilization is required, due to the common pathconfiguration for down-converted and pump photons.The past two decades have seen significant efforts dedicatedto improving the efficiency and tunability of SPDC sources. Inparticular the advent of periodic poling technology has greatlyextended the range of possible SPDC configurations, andmade it possible to engineer highly efficient collinear quasi-phase matching (QPM) in long periodically poled nonlinearcrystals [4, 10, 11, 13–17] and waveguide structures [18–23].In particular, SPDC sources that exploit the strong nonlinear ∗ [email protected] † Current address: Quantum Engineering Technology Labs, H. H. WillsPhysics Laboratory & Department of Electrical and Electronic Engineer-ing, University of Bristol, Merchant Venturers Building, Woodland Road,Bristol BS8 1UB, United Kingdom ‡ [email protected] interaction of collinear QPM with co-polarized pump, signal,and idler photons, so-called type-0 QPM, have resulted in thehighest entangled pair rates reported to date [4, 24]. Due to thespatial overlap of the SPDC and pump modes, however, thesetype-0 sources typically require wavelength distinguishabil-ity ( λ s ≠ λ i ) or non-collinear SPDC emission angles in or-der to route photons into distinct spatial modes for indepen-dent manipulation (e.g. using dichroic mirrors or fiber-Bragggratings). As this limits their applicability in QIP protocolsthat require indistinguishable photons, the question naturallyarises, how we may generate polarization-entanglement suchthat identical signal and idler photons are separated determin-istically. That is, conditional on the detection of a signal(idler) photon in one spatial mode, there should be, in prin-ciple, a unit probability of a corresponding detection of theidler (signal) photon in a conjugate spatial mode. In contrastto this ideal case, the widely used probabilistic separation ona beam splitter always results in an undesirable two-photoncomponent in its output ports.To tackle this issue, Chen et al. [25] proposed a determinis-tic quantum splitter that uses two-photon interference to pas-sively route photons into two spatial modes. The most widelyknown manifestation of two-photon interference is the Hong-Ou-Mandel (HOM) effect, where identical photons impingingon the input ports of a beam splitter bunch into either one orthe other output port. In a time-reversed analogy, interferenceof two indistinguishable photon pairs results in anti-bunchingin the output ports of the beam splitter, i.e. a suppression oftwo-photon components in each port. This quantum splitterapproach has since found applications in several experiments,in particular on integrated waveguide platforms [26, 27].Here we present a novel source configuration which ex-ploits time-reversed HOM interference to deterministicallyroute wavelength-degenerate polarization-entangled photonsinto two distinct spatial modes. By coherent superposition ofidentical photon pairs in four different modes on a polariza-tion beam splitter, our source yields polarization entanglementwithout any requirement for detection post-selection. This isachieved in a phase-stable manner by combining the benefitsof the popular polarization Sagnac sources and crossed-crystalsources. Using highly efficient collinear type-0 QPM in bulkperiodically poled potassium titanyl phosphate (ppKTP) crys-tals, we generate wavelength-degenerate photon pairs around
810 nm with a Bell-state fidelity of and detect a pairrate of
160 kcps per mW of pump power.This photon pair yield, which – to the best of our knowledge– is the highest value reported for a wavelength-degeneratepolarization-entangled photon source, is of particular rele-vance whenever the available pump power is limited, as isthe case in space-proof entangled photon sources for satellite-based quantum communication [28–30], or fundamental testsof quantum theory in scenarios with extreme link loss [31–33]. Moreover, the scheme can be extended to integratedsource platforms, where the separation of photons generatedin overlapping, co-propagating spatial modes is particularlychallenging.
Basic scheme.
To illustrate the operational principle of thesource (Fig. 1), let us consider a pair of identical photonswhich are either both linearly polarized along the diagonal oranti-diagonal direction. The photons are incident on a polar-ization beam splitter (PBS) in a state: ( a † D + e i φ a † A )√ ∣ vac ⟩ = ∣ D , 0 A ⟩ + e i φ ∣ D , 2 A ⟩ √ (1)where a † D = /√ ( a † H + a † V ) and a † A = /√ ( a † H − a † V ) rep-resent the creation operators for photons polarized diagonallyand anti-diagonally with respect to the rectilinear referenceframe of the PBS (Fig. 1(a)). The vacuum state is representedby ∣ vac ⟩ and φ represents a polarization-dependent phase fac-tor. Setting the relative phase φ = π , the state reads: ∣ D , 0 A ⟩ − ∣ D , 2 A ⟩ √ = ∣ H , 1 V ⟩ . (2)This can be seen as anti-bunching due to Hong-Ou-Mandelinterference in the orthogonal polarization modes [34, 35].The PBS then maps the orthogonally polarized photon pairsinto two distinct spatial modes: ∣ H , 1 V ⟩ → ∣ H ⟩ ′ ∣ V ⟩ ′ ≡ ∣ Ψ ( ) ⟩ , (3)where ∣ H ⟩ i ≡ ∣ H , 0 V ⟩ i and ∣ V ⟩ i ≡ ∣ H , 1 V ⟩ i denote hori-zontal and vertical single-photon polarization states in ports i = { ′ , 2 ′ } , respectively.Analogously, when two photons in a state (2) are incidentvia port 2 of the PBS (Fig. 1(b)) one obtains single photonswith the orthogonal polarization state: ∣ H , 1 V ⟩ → ∣ V ⟩ ′ ∣ H ⟩ ′ ≡ ∣ Ψ ( ) ⟩ , (4)Consequently, the coherent superposition of pair gener-ation possibilities ∣ Ψ ( ) ⟩ + ∣ Ψ ( ) ⟩ results in a maximallypolarization-entangled state in spatial modes 1’ and 2’: ∣ Ψ ⟩ ′ ,2 ′ = √ (∣ H ′ V ′ ⟩ + ∣ V ′ H ′ ⟩) . (5)In our realization of this operational principle we producepairs of photons in a state (1) by balanced pumping a pair ofcrossed crystals with a relative inclination about their com-mon propagation axis of ○ . By folding the configurationdepicted in Fig. 1 into a loop we realize spatial modes 1and 2 as the clockwise- and counter-clockwise propagationmodes of a PSI. The polarization-entangled state (5) is thenobtained by bi-directionally pumping the two crystals, whichare placed in the center of the loop. This implementation thusensures constant phases in states (1) and (5) without any re-quirement for active interferometric stabilization (changes ofthe optical path length are experienced by the pump drivingthe SPDC process as well as the emitted biphoton state). An-other benefit reveals itself when considering the multi-modespatio-temporal characteristics of the bi-photon wavepackets[36]; due to the symmetric Sagnac configuration, there is,in principle, no requirement to remove distinguishing arrival-time information (e.g. via birefringent compensation crystals)as it is never created in the first place. Hence, the scheme can,in principle, also be extended to large SPDC bandwidths, andeven non-degenerate wavelengths.Note that, while the scheme can also be realized using anon-polarizing beam splitter, the implementation with a PBSautomatically ensures that the correct polarizations are sortedinto the two output ports, thus improving the fidelity of thepolarization-entangled state. This feature can also be inter-preted as an entanglement purification step [37], wherein thestate impurity due to residual distinguishing information inthe interfering modes merely affects the anti-bunching prob-ability. Imperfect indistinguishability thus reduces the anti-bunching probability, and consequently the rate of joint de-tections in spatial modes 1’ and 2’. However, it should inprinciple not affect the quality of the polarization correlationsconditioned on a joint detection in these two modes. Experiment.
In our experimental realization of the sourcedesign (Fig. 2) a pair of crossed ppKTP crystals is placed in-side a Sagnac loop configuration and pumped with a
405 nm continuous wave grating-stabilized laser diode. A half-waveplate (HWP) in the pump beam is used to set a diagonal polar-ization state, such that both clockwise and counter-clockwisedirections of the interferometer are pumped equally. Toachieve the desired diagonal and anti-diagonal polarizationswithin the Sagnac loop, we designed an oven with a V-groovesuch that the two crossed crystals are oriented at ○ (seeinset of Fig. 2). Thus, the crystals are phase-matched forSPDC with diagonally and anti-diagonally polarized pumplight, respectively. The crossed-crystal configuration at thecenter of the loop is based on two mutually orthogonally ori-ented 11.48-mm-long ppKTP crystals. They provide type-0 collinear phase matching with pump (p), signal (s) andidler (i) photons at center wavelengths of λ p ≈
405 nm and λ s , i ≈
810 nm at a temperature of ○ C . Since the pumpbeam in the clockwise/counter-clockwise propagation direc-tion is horizontally/vertically polarized, it is equally likely to (a) PBS1
PBS 1' (b) à à PBSPBS PBS1 1' ((a)))
PBSPBS1
PBSPBS 1'
212 PBSPBS1 1' à ((((bb))) à PBSPBSPBSPBS PBSPBS1 1' H V A D FIG. 1. Illustration of the source’s principle. A pair of identical pho-tons in a correlated state is incident on a PBS via either input port1 (Fig. 1(a)) or 2 (Fig. 1(b)). As a consequence of time-reversedHOM interference of orthogonal polarization modes, the photonsanti-bunch into the output ports 1’ and 2’. Superposition of (a) and(b) thus results in a polarization-entangled state. H, V, A and D rep-resent horizontal, vertical, anti-diagonal and diagonal polarizations,respectively. generate a photon pair in the first crystal or the second crystal,resulting in a state of (1). The relative polarization phase wastuned by tilting a wave-plate (WP) with optical axis set at ○ .After combining the SPDC photon pairs from both prop-agation directions on the PBS, the down converted signaland idler photons in spatial mode 2’ are separated from thepump by using a dichroic mirror and coupled into single modefibers. Two long-pass filters are used to eliminate the remain-ing pump light and noise. Polarizers are used to evaluate po-larization correlations and bandpass filters are utilized to ad-just the spectral bandwidth of the generated entangled state.Finally, the down converted photons are detected by siliconavalanche photo diodes, and two-fold events are identified us-ing a fast electronic AND gate when two photons arrive at thedetectors within a coincidence window of ∼ . Results.
In order to evaluate the source brightness, we re-moved the polarizers from the setup and set the pump laserpower to approximately µ W . With two bandpass fil-ters in place, we detect a two-fold coincidence rate of R c ≈ mirror PBS pp K T P mirrro dHWP HWPWP LD DMmirror & T E C LPIFPOL
Detectors W x z y dH PCPPPPF OLLL P z (cid:262) z (cid:262) FIG. 2. Illustration of the crossed-crystal Sagnac source. LD: laserdiode; PBS: polarization beam splitter; dHWP: dual-wavelength halfwave plate; HWP: half wave plate; WP: wave plate; DM: dichroicmirror; ppKTP: type-0 periodically poled potassium titanyl phos-phate crystal; TEC: temperature controller; LP: long pass filter; IF:interference filter; POL: polarizer. The top left inset illustrates the ○ orientation of the oven which ensures that photon pairs are gen-erated either with diagonal or anti-diagonal polarizations. kcps and single count rates of R s ≈ R i ≈ kcps. This cor-responds to a normalized pair rate of 160 kcps/mW, a spectralbrightness of 53 kcps/mW/nm and a heralding efficiency of R c R s ≈ R c R i ∼ for the idler and signal photons.Next, we characterized the polarization entanglement bymeasuring the two-photon polarization interference contrastin two mutually unbiased bases. We observe fringe visibili-ties of V H / V = ( ) in the H/V basis and V A / D = ( ) in the A/D basis without (with) subtractionof accidental coincidences. These visibilities imply lowerbounds of F ≥ and C ≥ on the Bell-state Fidelityand Concurrence, respectively [38].We also assessed the source performance without the ad-ditional bandpass filters in place. Collecting photonpairs for the entire phase-matching bandwidth for wavelength-degenerate type-0 SPDC ( ∼
20 nm
FWHM), the normal-ized pair rate is increased to 1.07 Mcps/mW and the spectralbrightness remains essentially unchanged at kcps/mW/nm.However, the Bell-state fidelity is reduced to F ∼ , which indicates that there remains a residualdegree of distinguishability in the time-frequency domain.In a perfectly symmetric Sagnac loop, the relative phaseof clockwise and counter-clockwise propagating pairs shouldbe perfectly matched. We thus attribute the remaining wave-length dependent phase to non-ideal optical components; themost likely candidates being either polarization-dependentgroup velocity dispersion of the broad-band multi-layer mir-ror coatings, or the dual-wavelength PBS, which was designedfor a narrow wavelength range around
810 nm . We believethat it should be possible to obtain high visibility for the fullspectrum by incorporating appropriate zero-phase-shift opti- T w o − f o l d c o i n c i den c e ( kc p s ) V i s i b ili t y Correlated basesAnti−correlated basesVisibility
FIG. 3. Stability of our source over long time under laboratory condi-tions. The two-fold coincidence counts and visibilities in correlatedand anti-correlated A/D bases are stable on the order of hours, indi-cating its suitability for long-term operation in field experiments. cal components.To verify the long-time stability of our source, we per-formed measurements in the correlated and anti-correlatedA/D polarization bases over the course of an hour (Fig. 3).The results illustrate the good temporal stability of the sourceefficiency, as well as the quality of the entangled state, makingit a suitable source for long-term autonomous operation.
Discussion.
We have demonstrated a novel entangled pho-ton source configuration based on time-reversed HOM inter-ference to passively route indistinguishable photons into twospatial modes. The proposed source allows the use of effi-cient type-0 SPDC in bulk ppKTP in a wavelength-degenerateQPM scheme, without the usual requirement for detectionpost-selection. In particular, the recent advances in satellite-based quantum communication [28–30], and proposals forspace link experiments with extreme loss [31–33] have high-lighted the need for ultra-bright, resource-efficient quantumsources with compact footprint and long-term stability.Our source yields entangled photon rates in excess of pairs per second for pump powers readily attainable usingcompact laser diodes, making it an ideal candidate for a vari- ety of applications. We note that, using a more tightly focusedpump beam we could drastically improve the brightness; inprinciple, we expect our source to be capable of producingpair rates as high as those reported for non-degenerate phasematching [4, 14], which could be of particular relevance inthe development of ultra-bright space-proof entangled photonsources.While our experimental realization is based on bulk optics,the overall scheme could also be extended to integrated quan-tum sources, where the separation of co-propagating photonswith overlapping spatial modes poses a significant challenge.We also note that the time-reversed HOM could also be ex-tended to yield other forms of entanglement, e.g. frequency-polarization hyperentanglement or high-dimensional orbitalangular momentum entanglement [39]. Another promisingline of inquiry could address the combination with entangle-ment by path identity [40]. Finally, we also envisage the use ofthis approach in engineering multi-photon entanglement [41],where unbalanced beam splitting ratios could enable the fil-tration and tailoring of desired photon number characteristics[42, 43].In conclusion, we hope that our results will inspire new ex-perimental configurations based on multi-photon interference.We believe that fully harnessing HOM interference couldprovide valuable generating and detecting complex forms ofhigh-dimensional multi-photon entanglement, as required forthe next generation of multi-partite quantum information pro-cessing protocols.We thank Thomas Scheidl and Johannes Handsteiner forhelpful conversations and comments on the initial draft ofthe manuscript as well as Valerio Pruneri for providing pp-KTP crystals. YC thanks Lijun Chen for support. Finan-cial support from the Austrian Research Promotion Agency(FFG) Projects - Agentur f¨ur Luft- und Raumfahrt (FFG-ALRcontract 6238191 and 866025), the European Space Agency(ESA contract 4000112591/14/NL/US) as well as the Aus-trian Academy of Sciences is gratefully acknowledged. YCacknowledges personal funding from Major Program of Na-tional Natural Science Foundation of China (No. 11690030,11690032), National Key Research and Development Pro-gram of China (2017YFA0303700); the National Natural Sci-ence Foundation of China (No.61771236), and from a Schol-arship from the China Scholarship Council (CSC). [1] A. De Touzalin, C. Marcus, F. Heijman, I. Cirac, R. Murray,and T. Calarco, European Comission (2016).[2] M. Giustina, M. A. Versteegh, S. Wengerowsky, J. Handsteiner,A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.- ˚A. Lars-son, C. Abell´an, et al. , Physical review letters , 250401(2015).[3] L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst,M. A. Wayne, M. J. 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