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Physical Review A

Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing

Colin J. McKinstrie, Lasse Mejling, Michael G. Raymer, Karsten K. Rottwitt

Published May 22, 2012• 58 citations
Publisher

Abstract

Nondegenerate four-wave mixing driven by two pulsed pumps transfers the quantum state of an input signal pulse to an output idler pulse, which is a frequency-converted and reshaped version of the signal. By varying the pump shapes appropriately, one can connect signal and idler pulses with arbitrary durations and shapes. This process enables a variety of functions required by quantum information networks.

DOI
10.1103/physreva.85.053829

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Nondegenerate four-wave mixing driven by two pulsed pumps transfers the quantum state of an input signal pulse to an output idler pulse, which is a frequency-converted and reshaped version of the signal. By varying the pump shapes appropriately, one can connect signal and idler pulses with arbitrary durations and shapes. This process enables a variety of functions required by quantum information networks.
This thesis deals with applications of nonlinear four-wave mixing in the context of optical quantum information science. By enabling diverse functionalities such as single-photon generation, temporal shaping, and frequency conversion, four-wave mixing is a highly versatile tool for processing optical quantum information. The first part addresses the use of spontaneous four-wave mixing for generating entangled photon pairs with the particular property that the photons are uncorrelated in time and frequency. Two schemes are proposed to achieve this. The first proposal relies on a gradually varying interaction between two orthogonally polarized pump pulses in a birefringent waveguide. It is shown that, if the two pump pulses undergo a complete walk-through, the two generated photons emerge in orthogonal polarizations with uncorrelated- and tailorable time-frequency distributions. The second proposal deals with photon-pair generation in a microring resonator. In this setting, it is shown that a dual-pulse configuration can be used to excite- and subsequently de-excite the resonator on a sub-lifetime timescale. This turns out to strongly diminish time-frequency correlations. The second part considers the four-wave-mixing process Bragg scattering, which is known to enable noise-free frequency conversion. The Bragg-scattering process treated here, which occurs in a birefringent waveguide, is shown to allow for shape-preserving and strongly uni-directional conversion with a large acceptance bandwidth.
By utilizing the nondegenerate optical parametric amplifier, the quantum state transfer from a pump state with high frequency to a signal state of lower frequency is studied theoretically. The noiseless state transfer is characterized by frequency conversion efficiency and noise figure. It is shown that the quantum state can be well preserved during the frequency conversion as long as the optical parametric amplifier is operated far below the threshold, and meanwhile injected with an input idler field with a power density about ten times greater than that of the pump. The dependence of the noise figure and conversion efficiency on the idler amplitude, the analyzing frequency and the cavity extra loss is also discussed.
Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.