Quasiphasematched concurrent nonlinearities in periodically poled KTiOPO_4 for quantum computing over the optical frequency comb
Matthew Pysher, Alon Bahabad, Peng Peng, Ady Arie, Olivier Pfister
aa r X i v : . [ qu a n t - ph ] D ec Quasiphasematched concurrent nonlinearities in periodically poledKTiOPO for quantum computing over the optical frequency comb Matthew Pysher, Alon Bahabad, Peng Peng, Ady Arie, and Olivier Pfister , ∗ Department of Physics, University of Virginia, 382 McCormick Road, Charlottesville, VA 22904-4714, USA Department of Physics and JILA, University of Colorado at Boulder and NIST, Boulder, Colorado 80309, USA Department of Physical Electronics, Fleischman Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel ∗ Corresponding author: opfi[email protected]
Compiled November 2, 2018We report the successful design and experimental implementation of three coincident nonlinear interactions,namely ZZZ (“type-0”), ZYY (type-I), and YYZ/YZY (type-II) second harmonic generation of 780 nm lightfrom a 1560 nm pump beam in a single, multigrating, periodically poled KTiOPO crystal. The resultingnonlinear medium is the key component for making a scalable quantum computer over the optical frequencycomb of a single optical parametric oscillator. c (cid:13) OCIS codes:
Quantum computing is an exciting field driven bythe promise of exponential speedup of a priori arduouscomputational processes such as integer factoring [1, 2].Most proposals for experimentally implementing quan-tum computing call for the use of two-state quantumsystems, or qubits [3]. However, a quantum computercould very well use continuous quantum variables [4, 5],such as position and momentum, or the quadrature am-plitude operators of the quantized field [6–8]. Recently,some of us have proposed a new and extremely scalablemethod for building a quantum register by use of the setof quantum harmonic oscillators (“qumodes”) definedby a single optical resonator [9, 10]. In this proposal,the quantum correlations (entanglement) necessary forquantum computing will be implemented by a nonlin-ear medium placed inside the cavity, thereby realizing asophisticated optical parametric oscillator (OPO). Thesophistication stems from the fact that three differentsecond-order nonlinear interactions must be simultane-ously phasematched over the same set of cavity modes,i.e. must be concurrent. These interactions are paramet-ric downconversion ( λ/ λ ) of ZZZ (“type-0”), ZYY(type-I), and YYZ/YZY (type-II), where the first let-ter denotes the polarization of the pump field and thelast two letters denote the polarization of the signal (en-tangled) beams. In previous work [11], we demonstratedthe simultaneous quasi-phasematching (QPM) of this setof interactions at room temperature for λ = 1490 nm inperiodically poled KTiOPO (PPKTP) with a single pe-riod of 45 . µ m. This was a serendipitous discovery thatrelied upon a weak seventh-order QPM of the ZYY in-teraction (even though the final signal turned out to bemuch larger). Despite this result, designing concurrentnonlinear interactions remained difficult because the pre-cision on the Sellmeier coefficients, as well known as theyare, was still not high enough, in particular for n Y .In this Letter, we use Fourier engineering [12, 13] toachieve and demonstrate a concurrent design with low- order , hence efficient, QPM at λ = 1560 nm, close to theloss minimum of silica optical fibers. Recent advances insqueezing at and around this wavelength also make it areasonable choice [14, 15]. This 1560 nm design requiredthe use of three different poling periods. Two early it-erations used published Sellmeier equations [16–18]. Inthese initial versions, the ZZZ and ZYY QPM peaksoverlapped well at 1560 nm at room temperature butthe YZY interaction was quasi-phasematched for 1560nm between average temperatures of 248 . ◦ C (for a de-signed phase mismatch of 1 . × m − at room tem-perature) and 300 . ◦ C (for a designed phase mismatch of1 . × m − at room temperature). From these twomeasurements, and considering the corrections owing tothe temperature expansion of the crystal [18], we de-duced that the phase mismatch value of the YZY processshifts with temperature with a slope of 22 .
34 m − / K.This enabled us to predict the expected phase mismatchof the YZY interaction at 40 ◦ C to be 1 . × m − .However, owing to the uncertainty of this linear slopecorrection, we adopted a multi-section design for thecrystal. The 10 mm × × k ZZZ = 2 . × m − and ∆ k ZY Y =9 . × m − , we designed a quasiperiodic structurewith reciprocal base vectors k = ∆ k ZZZ + ∆ k ZY Y and k = ∆ k ZY Y such that the desired orders for phasematching the two processes are (1 , −
1) and (0 ,
1) inthis basis. Feeding these values into the algorithm ofthe dual grid method, we got the two tiling vectorsof the quasiperiodic structure to be of length 3 . µm and 2 . µm . The duty cycles used for the two build-1ng blocks of the structure were 0% and 100% respec-tively. This means that the 3 . µm building block isfabricated with a positive value of the nonlinear suscep-tibility, and the 2 . µm building block with a negativevalue. The Fourier coefficients given by this structurefor the ZZZ and ZYY processes are 0 .
112 and 0 . . .
3, 46 .
7, 47 .
2, and 47 . µ m in an attempt to correctlysample the wider range of QPM variation for the YZYinteraction. These periods are centered around the in-terpolated phase mismatch value of 1 . × m − =2 π/ . µ m that was obtained from the measurementswith the two previous samples. The ZZZ/ZYY QPM sec-tion was as wide as the crystal and overlapped with allYZY channels.The experimental study used second-harmonic gener-ation (SHG) with the setup shown in Fig. 1. The inputFig. 1. Experimental setup.1560 nm beam was emitted by a tunable fiber laser, am-plified by an erbium-doped fiber amplifier (EDFA), andthen collimated and sent through a chopper wheel thatallowed us to easily observe the SHG signal, amplitude-modulated at 450 Hz, on a fast-Fourier-transform signalanalyzer. After the chopper, the beam was sent througha half waveplate and polarizer, which allowed us to pre-cisely control the polarization of the input beam. Theinput beam was then focused to a waist radius of ap-proximately 30 µ m in the crystal, which was tempera-ture controlled to the nearest hundredth of a degree.Upon exiting the crystal, the input fundamental beamwas filtered out by a pair of long-pass filters that reflected99% of light in the 715–900 nm wavelength range whilepassing over 85% of light between 985 and 2000 nm. Be-fore reaching the detector, the SHG light passed through a half-waveplate and polarizing beam splitter combina-tion, which allowed us to choose the SHG polarizationto be detected. Any residual fundamental light was fil-tered by the very low detection efficiency of our siliconphotodiode at that wavelength. The detected light was S H G E ff i c i e n c y ( - W - ) Fig. 2. Temperature dependence of the YZY SHG signalfor each of the 5 channels. The poling periods used fromleft to right were 45.9, 46.3, 46.7, 47.2, and 47.7 µ m.measured by taking the average of ten measurements onthe signal analyzer and recording the signal at 450 Hz.The efficiency of the various nonlinear interactions wascontrolled by adjusting both the crystal temperature andthe wavelength of the input beam. The desired YZY pol-ing period fell in between the 45.9 and 46.3 µ m periodsthat were used to create our first two YZY channels.The other three YZY channels did not yield a significantSHG signal within the temperature range obtainable byour thermoelectric controller. Figure 2 shows the tem-perature dependence of the YZY SHG signal for each ofthe five YZY channels. S H G E ff i c i e n c y ( - W - ) Fig. 3. Triply concurrent SHG as a function of tempera-ture at 1560 nm in the 46 . µ m-period YZY channel.It appears that the 45 . µ m period corresponds to aQPM temperature larger than 65 ◦ C (which was the limitof our oven), while the 46 . µ m period is optimized justbelow 15 ◦ C. Despite the fact that none of our YZY chan-nels used the exact poling period needed to put the SHGpeak at 1560 nm at 40 degrees, the large temperatureacceptance bandwidth of YZY phase-matching (approx-imately 30 ◦ C × cm) yielded good overlap with the ZZZ2nd ZYY interactions, as can be seen from Fig. 3.Figure 4 shows results obtained using the YZY chan-nel with the 46 . µ m period, at a temperature of 37 ◦ C.A fit of the data shows the ZYY peak to occur at ex- S H G e ff i c i e n c y ( - W - ) Fig. 4. Triply concurrent SHG at 37 ◦ C in the 46 . µ m-period YZY channel.actly 1560 nm at this temperature, while the ZZZ peakoccurs at 1560.2 nm. The location of the beam waistin the crystal was adjusted so that the YZY SHG out-put matched that of ZZZ. When the waist was moved tomaximize YZY, the YZY near-peak efficiency (at 15 ◦ C,see Fig. 3) became approximately double that of thepeak ZZZ efficiency at 37 ◦ C. Using the aforementionedFourier coefficients and the values d = 15 . d = d = 3 .
75 pm/V [21], we obtain a ZYYto ZZZ peak-efficiency ratio of [(3 . × . / (15 . × . = 2 . / .
97 = 0 .
70, consistent with the exper-imental results of Figs. 3,4. For the YZY to ZZZ peak-efficiency ratio, we obtain [(3 . × /π ) / (15 . × . =5 . / .
97 = 1 .
92, again consistent with our experiment.This therefore confirms the values of Ref. 21. Note thatthe initial design used the different values d = 13 . d = 5 pm/V, which is why the ZYY inter-action ends up weaker than ZZZ, but this can clearly beremedied.In conclusion, we have designed and experimentallydemonstrated a PPKTP crystal with three concurrentphase-matchings at 1560 nm. The knowledge gainedabout the YZY QPM period in this work can now beapplied to generating a single Fourier-engineered grat-ing for all three processes [13]. Having a triply concur-rent crystal made with a single Fourier-engineered grat-ing gives several advantages over a crystal containingthree separate polings. In particular, the single gratingwould allow the crystal to be used in single-pass opera-tions, such as those using a nonlinear waveguide, ratherthan an optical cavity. For example, just using the simul-taneous ZZZ and ZYY phase-matchings in the Fourier-engineered crystal of this work could yield a useful sourceof collinear polarization-entangled photon pairs. Notethat this method could also be used to make a crystalwith four concurrent phase matchings in other materi-als, such as LiNbO and LiTaO . Last but not least, and most importantly here, the crystal in this study repre-sents the key component in the implementation of quan-tum computing over the optical frequency comb [9, 10],which is, in theory, extremely scalable.MP, PP, and OP were supported by U.S. NationalScience Foundation grants Nos. PHY-0555522, CCF-062210, and PHY-0855632. AA was supported by theIsrael Science Foundation, grant no. 960/05 and by theIsraeli Ministry of Science, Culture and Sport. References
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