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Quantum optical measurement of arbitrary fourth-order field moments via balanced homodyne correlation

Milena Gödecke

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Balanced homodyne correlation allows the measurement of moments of creation and annihilation operators with unequal or equal powers with high signal to noise ratios, thus giving access to high order moments. In this work we implement this method for the first time. Our realisation with eight detectors gives access to field moments up to fourth order. We use a laser direct written waveguide structures to implement the beam splitter cascade, and we use a photodiode array for multi-beam detection. The set-up is successfully verified with squeezed- and coherent states.

DOI
10.18453/rosdok_id00005556

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Balanced homodyne correlation allows the measurement of moments of creation and annihilation operators with unequal or equal powers with high signal to noise ratios, thus giving access to high order moments. In this work we implement this method for the first time. Our realisation with eight detectors gives access to field moments up to fourth order. We use a laser direct written waveguide structures to implement the beam splitter cascade, and we use a photodiode array for multi-beam detection. The set-up is successfully verified with squeezed- and coherent states.
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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.
Three different noise moments of field strength, intensity, and their correlations are simultaneously measured. For this purpose a homodyne cross-correlation measurement [1] is implemented by superimposing the signal field and a weak local oscillator on an unbalanced beam splitter. The relevant information is obtained via the intensity noise correlation of the output modes. Detection details like quantum efficiencies or uncorrelated dark noise are meaningless for our technique. Yet unknown insight in the quantumness of a squeezed signal field is retrieved from the anomalous moment, correlating field strength with intensity noise. A classical inequality including this moment is violated for almost all signal phases. Precognition on quantum theory is superfluous, as our analysis is solely based on classical physics.
Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.
A method is introduced that allows one to measure normal-ordered moments of the displaced photon-number operator up to higher orders, without the need of photon-number resolving detectors. It is based on unbalanced homodyne correlation measurements, with the local oscillator being replaced by a displaced dephased laser. The measured moments yield a simple approximation of quasiprobabilities, representing the full quantum state. Quantum properties of light are efficiently certified through normal-ordered observables directly accessible by our method, which is illustrated for a weakly squeezed vacuum and a single-photon-added thermal state.