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arXiv:quant-ph/9808052

Quantum-Non-Demolition Endoscopic Tomography

Mauro Fortunato, Paolo Tombesi, Wolfgang P. Schleich

Published Aug 26, 1998• 0 citations
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Abstract

We present a new indirect method to measure the quantum state of a single mode of the electromagnetic field in a cavity. Our proposal combines the idea of (endoscopic) probing and that of tomography in the sense that the signal field is coupled via a quantum-non-demolition Hamiltonian to a meter field on which then quantum state tomography is performed using balanced homodyne detection. This technique provides full information about the signal state. We also discuss the influence of the measurement of the meter on the signal field.

DOI
10.48550/arxiv.quant-ph/9808052

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We present a new indirect method to measure the quantum state of a single mode of the electromagnetic field in a cavity. Our proposal combines the idea of (endoscopic) probing and that of tomography in the sense that the signal field is coupled via a quantum-non-demolition Hamiltonian to a meter field on which then quantum state tomography is performed using balanced homodyne detection. This technique provides full information about the signal state. We also discuss the influence of the measurement of the meter on the signal field.
Any measurement scheme involving interference of quantum states of the electromagnetic field necessarily mixes information about the spatiotemporal structure of these fields and quantum states in the recorded data. We show that in this case, a trade-off is possible between extracting information about the quantum states and the structure of the underlying fields, with the modal overlap being either a goal or a convenient tool of the reconstruction. We show that varying quantum states in a controlled way allows one to infer temporal profiles of modes. Vice versa, for the known quantum state of the probe and controlled variable overlap, one can infer the quantum state of the signal. We demonstrate this trade-off by performing an experiment using the simplest on–off detection in an unbalanced weak homodyning scheme. For the single-mode case, we demonstrate experimentally inference of the overlap and a few-photon signal state. Moreover, we show theoretically that the same single-detector scheme is sufficient even for arbitrary multi-mode fields.
We discuss some theoretical and experimental aspects of quantum non-demolition (QND) measurements in the optical domain. The efficiency of a QND measurement can be characterized using three criteria, which describe respectively the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state-preparation criterion). Quantitative limits can be defined with respect to these criteria, delimiting "classical" and "quantum" domains of operation. We describe the implementation of two experiments which fulfill these criteria, using either three-level atoms inside a doubly-resonant optical cavity, or semiconductors emitters and receivers.
We perform quantum non-demolition (QND) photon counting on a microwave field trapped in a very high Q superconducting cavity, employing circular Rydberg atoms as non-absorbing light probes. Beyond realizing fundamental tests of quantum measurement theory, we use this QND method to prepare non-classical Fock and Schrodinger cat states of the field and to reconstruct their Wigner functions. Monitoring the evolution of these functions provides a direct observation of the decoherence process. Quantum feedback procedures will enable us to steer the field towards target states and to protect them against decoherence.
We introduce a method for quantum-state tomography for a pair of optical modes, which we call generalized rotations in phase space. Rather than using a dual-mode local oscillator field for implementing balanced-homodyne detection, as in previous methods, a single-mode local oscillator field can be used in our method, greatly simplifying certain aspects of experiments. The signal field is put through a series of general transformations before entering the detection system where quantum statistics are measured.