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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

A balanced homodyne detector and local oscillator shaping for measuring optical Schrödinger cat states

Thomas Gerrits, Scott Glancy, Sae Woo Nam

Published Apr 27, 2011• 5 citations
Publisher

Abstract

We present our implementation of an optical homodyne detector used to measure optical Schrödinger cat states. We show how we minimized the losses and mode-mismatches associated with homodyne detection, which become important when measuring non-classical states of light. We present a pulse-shaping scheme applied to the local oscillator to improve its temporal mode overlap with the non-classical state.

DOI
10.1117/12.885486

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We present our implementation of an optical homodyne detector used to measure optical Schrödinger cat states. We show how we minimized the losses and mode-mismatches associated with homodyne detection, which become important when measuring non-classical states of light. We present a pulse-shaping scheme applied to the local oscillator to improve its temporal mode overlap with the non-classical state.
The homodyne detection is one of the most basic tools for identifying the quantum state of light. It has been used to detect useful non-local properties, such as entanglement for the quantum teleportation and distillability of a secret key in quantum key distribution. In so doing, the detection scheme employs a bright optical pulse, called the local oscillator (LO) pulse, and the LO pulse is usually transmitted along with the signal pulses. The LO pulse is presumed to be a coherent state with an infinite intensity. However, it is difficult in practice to hold this presumption owing to noise in the optical transmission channels or an intervention by a malicious third party. As a result, the implementation may no longer be the homodyne detection, and those outcomes may merely disguise successful detection of entanglement or a secret key. Here, we present an alternative scheme that works as the homodyne detection to detect the non-local properties of light in a verifiable manner, without any presumption for the LO pulses. This scheme is essentially based on the same setup as the conventional implementation for the homodyne detection. This result contributes to close any possible loophole in the homodyne detection caused by the deviation from the ideal LO pulses.
This thesis reports the realization and applications of a versatile wideband balanced homodyne detector operating in the time domain and intended for Quantum Optical Tomography. The detector can work with high repetition rate lasers used for the production and measurement of the electric field quadratures of quantum states of light. Full characterization of the detector by shot-noise measurements and by verifying its capability to reconstruct the density matrix and Wigner function of various states of interest is given. By overcoming photodiodes response mismatch, high frequency electronics issues and by choosing an appropriate optical set-up, a high level of common mode suppression (52.4dB) and a low electronic noise gave a shot-to-electronic noise ratio of I3dB for a Local Oscillator with 6.2 x 108 photons-per-pulse on a ~ 100MHz bandwidth. Results for the characterization of a single-photon Fock state are presented. An average efficiency of 56% was obtained for the generation/detection of the state.
Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classical light fields in well-defined ultrashort optical pulse modes.
The balanced homodyne detector is the paradigm of phase-sensitive detection schemes in quantum optics. We study the effects of a quantum local oscillator in a coherent state for this detector when it is coupled to a single signal mode. We calculate explicit general expressions for the output statistics of the difference current of this detector (applicable even to non-classical states), and compare them to the statistics of the so-called quadrature-phase amplitude. We show that the naive condition that the number of quanta in the local oscillator be much larger than the number in the signal is not sufficient to ensure that the homodyne detector approximates an ideal detectorof the quadrature-phase amplitude, further, we derive explicit conditions for this approximation to be achieved when the signal is a coherent state or a superposition of coherent states.
The technique of dc-balanced, pulsed homodyne detection for the purpose of determining optical-field statistics on short time scales is analyzed theoretically. Such measurements provide photon-number and phase distributions associated with a repetitive signal light field in a short time window. Time- and space-varying signal and local-oscillator pulses are treated, thus generalizing earlier treatments of photoelectron difference statistics in homodyne detection. Experimental issues, such as the effects of imperfect detector balancing on (time-integrated) dc detection and the consequences of background noise caused by non-mode-matched parts of the multimode signal field, are analyzed. The Wigner, or joint, distribution for the two field-quadrature amplitudes during the sampling time window can be directly determined by tomographic inversion of the measured photoelectron distributions. It is pointed out that homodyne detection provides a new method for the simultaneous measurement of temporal and spectral information. Although the theory is generally formulated, with both signal and local-oscillator fields being quantized, emphasis is placed on the limit of a strong, coherent local-oscillator field, making semiclassical interpretation possible.
Light has a high carrier frequency of hundreds of THz and has the potential to realize ultrafast quantum information processing. Time-domain multiplexed continuous-variable optical quantum computation has recently attracted much attention [1]. In this method, it is important to encode optical quantum states in wavepackets with short temporal widths because the width of the quantum state determines the clock frequency of the computation. So far, in the continuous-wave (CW) light field, this wavepacket width has been limited by the bandwidth of homodyne measurements, which read out the quadratures of the quantum state. Recently, a technique using phase-sensitive amplifiers (PSAs) and broadband homodyne detectors with CW light has been developed [2]. Using that, the wavepacket width of quantum entangled states was successfully shortened to the picosecond scale [3]. However, the wavepacket width of the Schrödinger cat state, which is a phase-sensitive non-Gaussian state, was limited to the sub-nanosecond scale due to the timing jitter of the photon detector [4].