ОПТИКА И СПЕКТРОСКОПИЯ, 2010, том 108, № 2, с. 196-200
КВАНТОВАЯ ИНФОРМАТИКА ^^^^^^^^^^^^ ПЕРЕПУТАННЫЕ СОСТОЯНИЯ
УДК 535.14
A SINGLE-CRYSTAL SOURCE OF PATH/POLARIZATION ENTANGLEMENT
AT NON-DEGENERATE WAVELENGTHS
© 2010 S. Sauge and M. Swillo
Department of Microelectronics and Information Technology, Royal Institute of Technology, Kista, SE-16440 Sweden Received August 3, 2009
Abstract —We demonstrate a bright, narrowband, compact, quasi-phase-matched single-crystal source generating path-polarization-entangled photon pairs at 810 nm and 1550 nm at a maximum rate of 3 x 106 s-1 THz mW after coupling to single-mode fiber, and with two-photon interference visibility above 90%. While the source can already be used to implement quantum communication protocols such as quantum key distribution, this work is also instrumental for narrowband applications such as entanglement transfer from photonic to atomic qubits, or entanglement of photons from independent sources.
INTRODUCTION
Two-photon entangled states manifest one of the most striking phenomena at the heart of quantum mechanics. They have been used to demonstrate the violation of Bell inequalities and thus exclude local realism from the quantum theory [1, 2]. They now constitute an integral resource for the implementation of quantum information protocols, such as quantum key distribution [3], quantum teleportation [4, 5], or all-optical quantum computing [6—8]. They are also instrumental for precision measurements beyond the standard quantum limit [9].
Different approaches can be considered to create entangled photon pairs. Promising networkable sources under development generate photons directly in single-mode fibers [10, 11] or photonic crystal fibers [12] by means of four-wave mixing. Other emerging sources use semiconductor components with the prospect of integration on optical chips. Progresses have thus been reported with sources based on biexciton cascade of a quantum dot [13] or spontaneous parametric down-conversion (SPDC) and phase matching in semiconductor waveguides [14] or non-linear photonic crystals [15]. While those sources have the potential of increasing the generation efficiency, the most practical and spectrally bright sources to date are based on SPDC in non-linear dielectric quasi-phase matched (QPM) crystals [16—18] and waveguides [19, 20], for which the periodic modulation of the x(2) non-linearity allows collinear, wavelength-tunable emission of the photon pairs.
SPDC can be used under type-I (co-polarized outputs) or type-II (orthogonally polarized outputs) phase matching. Bi-directionnal pumping of one single crystal provides quasi-spectral and spatial indistin-guishability between counter-propagating pairs, and given that temporal indistinguishability is also ensured
between them, photons can be entangled in polarization, resulting in states of the form \HH) + e'? | VV) (type-I) or \HV) + e"?\VH) (type-II), where Hand V denote horizontal and vertical polarizations, respectively, and 9 is the output phase factor, which can be tuned to generate any of the four maximally entangled Bell states. Incidentally, the existence of a fixed phase relation between the two terms relies on the impossibility of deducing the polarization of a photon from any of its other properties after recombination of the two interfering paths.
In the case of type-II SPDC, inserting the non-linear crystal inside a Sagnac interferometer provides an intrinsically phase-stable source [21—24], because both counter-propagating beams travel the same loop structure, so that any change of path length in the loop is experienced by both beams, resulting in stable interferences. While it was claimed that such a setup could work with photon pairs created at non-degenerate wavelengths, experimental realizations so far have been limited to operation near degeneracy [21— 24].
In this paper, we present a type-I QPM single-crystal source of entangled photons operating at non-degenerate wavelengths. Photons are entangled in path and polarization at 810 and 1550 nm, respectively. The path-entanglement configuration at 810 nm leads to a very compact setup, while the use of polarization coding at 1550 nm with only 0.8 nm bandwidth makes the fiber-coupled source potentially suitable for long-distance quantum communication in field experiments, in view of the possibility to achieve real-time polarization control of each flying qubit, as proposed recently [25], by means of two narrow-spaced reference signals multiplexed in wavelength with the narrowband quantum channel. The single-crystal source has a spectral brightness of 3 x 106 s-1 THz-1 mW-1 after coupling to
A SINGLE-CRYSTAL SOURCE OF PATH/POLARIZATION
197
Fig. 1. Single crystal source of entangled photons at 810 and 1550 nm.
single-mode fiber, about ten times larger than the one previously reported for operation at non-degeneracy [17], with similar two-photon interference visibility above 90%, and a reduced number of components. While the setup is no more intrinsically phase-stable, the source configuration nevertheless provides the means to lock the phase by active stabilization of a Mach—Zehnder interferometer traveled by the pump light, as will be shown. This is a further improvement in contrast to [17]. Providing a narrower bandwidth of tens of pm, which could be achieved in the same configuration with a cavity-inserted waveguide, the source could also be used for applications such as entanglement transfer from photonic to narrowband atomic qubits at around 800 nm [26], or entanglement of (temporally indistinguishable thus narrowband) photons from two independent sources [27], as required for the realization of a quantum repeater.
THE SOURCE
The source is drawn in Fig. 1. We use a 50 mm-long type-1 bulk crystal made of periodically poled (PP) lithium niobate PPLN:MgO with a grating period of 7.5 |im (HC-Photonics). The crystal is pumped by two focused counter-propagating beams driven by a diode laser operating at a wavelength of 532 nm (Cobolt). The source has collinear emission at the non-degenerate wavelengths of Xs = 810 nm for the signal and X j = = 1550 nm for the idler, allowing efficient single-photon detection and low attenuation in fibers at telecom wavelength, respectively (wavelength tuning can be achieved by varying the temperature of the brass oven heating the crystal at around 100°C with 0.1°C stability).
The pump is focused into the crystal by an achromatic lens (f = 150 mm) and split in two orthogonal
beams by a polarizing beam-splitter (PBS). The intensity of the pump along the two arms is balanced by means of a half-wave plate (HWP) set before the PBS. Since the crystal only down-converts pump light having a polarization of the electromagnetic field set along the crystal's optical axis, a second HWP is used along one of the two pump arms in order to undo the polarization rotation induced by the PBS. The signal and idler are generated with vertical (V) polarization. For the pump beam, we estimated a waist at the focus point
2
of 2w0 = 250 |m, giving a Rayleigh range z0 = nw0 / X of about 90 mm in PPLN:MgO, hence a z0/L ratio of 1.8.
The two counter-propagating idler beams generated at 1550 nm are recombined at the PBS splitting the pump, after rotation of the polarization in one of the two arms by the same HWP used to adjust the polarization of the pump beam. Both PBS and HWP are optimized for idler wavelength only because the resulting intensity imbalance between the vertically-polarized components of the two pump beams down-converting in the crystal can be compensated by adjusting the HWP at 532 nm, and by increasing the pump power. After the PBS, the idler is separated from pump by means of a dichroic mirror, filtered from residual pump light by an isolator, coupled to 100 meters of single-mode fiber after which one analyzes the polarization state of the qubit with a PBS and a motorized HWP used for the purpose of recording two-photon visibility curves. A polarization controller is used to align the polarization at the output of the fiber with respect to the analyzer. The bandwidth of the 1550 nm photon after coupling to single mode fiber, as measured by a spectrograph at full pump power without conditional gating, is 0.8 nm FWHM, compatible with 100 GHz wavelength multiplexing.
Pump
Fig. 2. Principle of active stabilization of the single-crystal source. The output phase factor 9 = ks(-AL(- + ALs) can be set by locking the path mismatch (-ALj + ALs) of the Mach—Zehnder interferometer (MZI) traveled by pump light between the polarizing beam splitter where it is split until the non polarizing beam splitter after which pump interferences can be monitored with photodiodes Det 1 and Det 2. For a preliminary alignment of the interferometer, we used a broadband source at 1550 nm and we looked at the output of the MZI with a spectrometer. Interferences modulate the continuous spectrum of the broadband source with oscillations, which get broader as the MZI gets balanced. The nearly equal-arm-length point is reached by means of a piezo nano-positioning actuator mounted on the interfering beam-splitter. The piezo-actuator is then used to tune the output phase factor to -n/2 for which maximum correlations are observed.
The two signal beams generated at 810 nm are separated from the pump beams by dichroic mirrors positioned near the exit of the QPM crystal, and the correlations shared with idler photons are mapped onto the four output ports of three non-polarizing beam-splitters (BS) before coupling to one of four avalanche photo-detectors (Si APD) labeled H, V, D and A, in relation to the horizontal (H), vertical (V), diagonal (D) and anti-diagonal (A) polarization states of the idler qubits measured at 1550 nm in the two conjugate basis H/V and D/A, which in this case are selected by rotation of the HWP, see Fig. 1.
If APD "H" or "V" clicks when detecting a photon at 810 nm, the transmitte
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