A folded-sandwich polarization-entangled two-color photon pair source with large tuning capability for applications in hybrid quantum systems
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Abstract
We demonstrate a two-color entangled photon pair source which can be adapted easily to a wide range of wavelength combinations. A Fresnel rhomb as a geometrical quarter-wave plate and a versatile combination of compensation crystals are key components of the source. Entanglement of two photons at the Cs D1 line (894.3 nm) and at the telecom O-band (1313.1 nm) with a fidelity of \(F=0.753 \pm 0.021\) is demonstrated, and improvements of the setup are discussed.
Keywords
Bell State Nonlinear Crystal Photon Pair Entangle Photon Volume Bragg Grating1 Introduction
Scheme of entanglement distribution via a two-color entangled photon source. a Two Bell-state measurements (BSM) on photons from two stationary qubit/flying qubit entangled systems and two photons from a two-color entangled photon source establish entanglement between two stationary qubits. b Similarly, a single Bell-state measurement on a photon from a stationary qubit/flying qubit entangled system and one photon from a two-color entangled photon source establish entanglement between the stationary qubit and a telecom photon
Different schemes of two-color collinear entangled photon pair sources using type-0 down-conversion. A horizontally (vertically) polarized pump photon in an appropriate, i.e., horizontal (vertical), crystal creates horizontally (vertically) polarized signal and idler photons. No photons are created when pump polarization and crystal orientation are orthogonal. a The two possible paths in the two-crystal Sagnac configuration. In the clockwise and counterclockwise path, the photon pair is generated in the second crystal. In the (counter) clockwise path, the photon pair is generated vertically (horizontally) because the second crystal has horizontal (vertical) orientation. b The two paths in the crossed-crystal configuration. The first photon pair (vertically polarized) is created in the first crystal and accumulates an extra phase while passing through the second crystal. The second photon pair is created in the last crystal, just as the counterclockwise photon in the Sagnac configuration. c Folded-sandwich configuration. The polarization rotation element and a mirror (both depicted as one gray box) rotate and reflect the first pair. This is equivalent to the first pair in the crossed-crystal scheme, only that instead of the crystal the light polarization is rotated. In the folded-sandwich configuration, the second crystal is the mirrored first crystal. The (diagonal or unpolarized) pump beam is depicted in green
The rotation of the second crystal in the crossed-crystal configuration (Fig. 2b) can be replaced by a half-wave plate. Replacing the half-wave plate and the second crystal by a quarter-wave plate and a mirror yields the folded-sandwich scheme (Fig. 2c). Using only a single nonlinear crystal makes it considerably easier to avoid the leakage of which-crystal information. The folded-sandwich and the crossed-crystal configuration include a compensation crystal, which compensates the additional dispersion, whereas this is not needed in a two-crystal Sagnac configuration.
Together with the pump, any two-color entangled photon source involves three fields of widely different wavelengths. This imposes strong constraints on dispersion compensation. In particular, a source for generating entanglement in quantum hybrid systems should be easy to align, intrinsically stable and tunable in order to account for various transition frequencies. The Sagnac configuration requires a special three-color beam splitter and is very difficult to align [14]. The crossed-crystal configuration lacks the phase stability of the Sagnac configuration. Therefore, it is desirable to use the simpler folded-sandwich configuration. In this paper we show for the first time how the folded-sandwich can be used to generate highly non-degenerate photons. To this end, we slightly modify the folded-sandwich configuration. In contrast to previous work, we employ geometrical, i.e., wavelength-independent, polarization manipulation.
Here, we target for a two-color entangled photon source at \(\lambda _{\text {s}}=894.3\,\hbox {nm}\) and \(\lambda _i=1313.1\,\hbox {nm}\). These two wavelengths correspond to the Cs D1 line and the telecom O-band, respectively. The former has been chosen on the one hand as a convenient standard atomic transition. On the other hand, it is also accessible with excitonic transitions in InGaAs quantum dots [15]. The source is thus applicable for quantum hybrid systems [16, 17] involving atomic species, semiconductor quantum dots or molecules as well as long-distance transfer via optical fibers. Here we aim on long-distance transfer of qubits from quantum dots.
2 Setup
Setup based on one periodically poled lithium niobate crystal (ppLN) doped with approximately 5 % magnesium oxide (MgO), of length \(L=40\,\hbox {mm}\). The crystal temperature is controlled via a crystal oven (not shown). The Fresnel rhomb acts as a geometrical quarter-wave plate. The concave mirror (CM) reflects the light back into the crystal. The focusing (L1) and collimation (L2) lenses adjust the beam width. The first dichroic mirror (DM1) separates pump and down-converted photons. The second dichroic mirror (DM2) separates signal and idler photons. The phase compensation crystal consists of several \(\hbox {YVO}_4\) slabs to allow for dispersion control for a broad range of wavelengths. Both crystal ovens are omitted in this figure [18]
The diagonal pump beam and the horizontally polarized pair pass the nonlinear crystal a second time. Again, the vertical part of the diagonal pump beam may create a vertically polarized pair. The pump power is chosen such that the probability for creating more than one pair per double-pass is low. The pump polarization is chosen such that the count rate is the same for detection in the horizontal and vertical basis. Slight differences in the creation probability in the first and the second pass can be compensated by adjusting the pump polarization. The pump beam and the created photons are separated at the dichroic mirror (DM1). The photon pair is then collimated (L2) and directed onto a compensation crystal. Finally, signal and idler photons are separated at a dichroic mirror (DM2). In each of the separate arms, wave plates and polarizers allow for measurement of different polarization states. Each arm is coupled to a single-mode fiber. The fibers can either be connected to a spectrograph or to avalanche photodiodes (APDs) for spectral or coincidence measurements.
There are different values for the birefringent properties of \(\hbox {YVO}_4\) in the literature. Table 1 lists the refractive index difference of the ordinary and extraordinary axis of \(\hbox {YVO}_4\) and the calculated length of a compensation crystal for the wavelengths \(\lambda _{\text {s}}=894.3\,\hbox {nm}\) and \(\lambda _i=1313.1\,\hbox {nm}\) for different sources. For the values that Zelmon et al. provide [20], Fig. 4 shows the calculated phase \(\phi + \tilde{\phi }\) as a function of the wavelength for two different lengths of the compensation crystal. The two target wavelengths \(\lambda _{\text {s}}=894.3\,\hbox {nm}\) and \(\lambda _i=1313.1\,\hbox {nm}\) are plotted as vertical lines.
Reported refractive index difference \(\Delta n=n_{\text {e}}-n_{\text {o}}\) of the ordinary and extraordinary axis of \(\hbox {YVO}_4\) from different sources and the calculated corresponding length of compensation crystal for \(\lambda _{\text {s}}=894.3\,\hbox {nm}\) and \(\lambda _i=1313.1\,\hbox {nm}\)
Calculated phase \(\phi +\tilde{\phi }\) as a function of the wavelength for two different lengths of the compensation crystal (constant offset subtracted). A flat phase is obtained for \(\tilde{L}=154\,\hbox {mm}\) (solid line) for the two target wavelengths \(\lambda _{\text {s}}=894.3\,\hbox {nm}\) and \(\lambda _i=1313.1\,\hbox {nm}\) (vertical lines). The plateaus of the flat phases are shifted considerably for \(\tilde{L} = 153\,\hbox {mm}\) (dashed line). Based on refractive index data reported by Zelmon et al. [20]
Spectra of signal photons for different temperatures of the nonlinear crystal. The decreasing intensities with higher temperatures are due to decreasing sensitivity of the spectrometer CCD camera. At 1064 nm, the signal and idler photons are degenerate
3 Determining the optimal crystal length
Measured coincidence counts as a function of the orientation of the half-wave plate in different bases combinations. The dashed and solid lines are fits to sine functions. The resulting visibilities \(v_i\) from Eq. (15) are indicated
The procedure to find the right compensation crystal relies on measuring polarization-sensitive coincidence counts as a function of the orientation of the half-wave plate \(\theta _{{\text {HWP}}}\) in one arm. Fig. 6 shows such measurements in different bases combinations. The measured curve can be fitted to a sine function, and the visibility can be derived (see next Section for details). Then, thin slabs of \(\hbox {YVO}_4\) are added, until the visibility cannot be enhanced further. In this way, an optimum total length of the compensation crystal can be found.
Measured coincidence counts in the \(|AA\rangle\) basis (both polarizers anti-diagonal) as a function of the temperature of a 30 mm compensation crystal slab. The total crystal length is 153 mm
In order to do this, we changed the temperature of a 30 mm compensation crystal slab. Figure 7 shows the measured coincidence counts between signal and idler photons in the \(|AA\rangle\) basis as a function of the temperature of the compensation crystal. We find a phase shift of \(\pi\), i.e., between two different Bell states, for \(\sim 2.4\,^\circ \hbox {C}\) temperature difference.
For the wavelengths \(\lambda _{\text {s}}=894.3\,\hbox {nm}\) and \(\lambda _i=1313.1\,\hbox {nm}\) we find a optimal total crystal length of \(L=153\,\hbox {mm}\). The total length was composed of 7 slabs \(\hbox {YVO}_4\) of 2 cm length and one slab of 1 cm, 2 mm and 1 mm length. The total length is close to some of the reported data on the refractive index of \(\hbox {YVO}_4\) in the literature [20], even though they investigated 0.5 % Nd-doped \(\hbox {YVO}_4\). However, it deviates from the value reported by other studies [21], as well as from the manufacturer specification (Foctek Inc.) [19].
With the experimentally determined crystal parameters, it is in principle straightforward to estimate the compensation crystal length also for other pairs of wavelengths. Additional crystal slabs can be added or removed allowing for a wide tuning range.
4 Verifying entanglement
5 Conclusion
We demonstrated a novel folded-sandwich scheme for the generation of two-color entangled photons which uses a Fresnel rhomb as a geometrical quarter-wave plate. By this, all optical components are more easily adapted to wide combinations of wavelengths. For example, no three-color beam splitters as in a Sagnac configuration are required. Adjusting the compensation crystal length offers a tuning capability over more than 100 nm. Our source is a viable tool to provide highly non-degenerate entangled photons for quantum hybrid systems, in particular when solid-state emitters with an a priori unpredictable transition frequency are involved.
Notes
Acknowledgments
This work was funded by BMBF (Q.com-H). Funding by DFG through SFB 787 is acknowledged by O.D. O.D. likes to thank Sven Ramelow, Fabian Steinlechner and Amir Moqanaki for their hospitality during his stay in Vienna and their continuous input and support on the experimental design. This work was also supported by project EMPIR 14IND05 MIQC2 (the EMPIR initiative is co-funded by the European Union’s Horizon 2020 research and innovation programme and the EMPIR Participating States).
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