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Physical Review Letters

Adaptive Quantum Nondemolition Measurement of a Photon Number

Bruno Peaudecerf, T. Rybarczyk, Stefan Gerlich, S. Gleyzes, J. M. Raimond, S. Haroche, I. Dotsenko, M. Brune

Published Feb 26, 2014• 25 citations
Publisher

Abstract

In many quantum measurements, information is acquired incrementally by the successive interaction of meters with the measured system. Adaptive measurements minimize the use of resources (meters) by adjusting the measurement settings according to available information. We demonstrate an adaptive measurement for nondestructive photon counting in a cavity, based on Ramsey interferometry for Rydberg atoms interacting with the field. Tuning the interferometer in real time, we speed up the measurement by up to 45%. Such adaptive methods are promising for quantum metrology, state preparation, and feedback.

DOI
10.1103/physrevlett.112.080401

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In many quantum measurements, information is acquired incrementally by the successive interaction of meters with the measured system. Adaptive measurements minimize the use of resources (meters) by adjusting the measurement settings according to available information. We demonstrate an adaptive measurement for nondestructive photon counting in a cavity, based on Ramsey interferometry for Rydberg atoms interacting with the field. Tuning the interferometer in real time, we speed up the measurement by up to 45%. Such adaptive methods are promising for quantum metrology, state preparation, and feedback.
We describe the optimum detection procedure to follow in order to measure by atomic interferometry the number of photons present in a cavity by using a Quantum nondemolition scheme. The method we discuss is the one recently introduced by Brune et al. [1, 2], in which the field intensity is detected by recording atomic interferences in a Ramsey type set up. A succession of two-level atoms interacts with the cavity field which is the analog of a birefringent retarding plate for the atomic wave function. The information is acquired in the form of binary digits (atoms detected in one level or the other). We discuss an optimal strategy which yields the value of the photon number with a number of atoms of the order of the base 2 logarithm of the field photon number dispersion. The procedure described here is the one we intend to use in an experiment in preparation.
We present a protocol for probing the state of a quantum system by its resonant coupling and entanglement with a meter system. By continuous measurement of a time evolving meter observable, we infer the evolution of the entangled systems and, ultimately, the state and dynamics of the system of interest. The photon number in a cavity field is thus resolved by simulated monitoring of the Rabi oscillations of a resonantly coupled two-level system, and we propose to regard this as a practical extension of quantum nondemolition measurements with applications in quantum metrology and quantum computing.
A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described in detail. It is based on the detection of the dispersive phase shift produced by the field on the wave function of nonresonant atoms crossing the cavity. This shift can be measured by atomic interferometry, using the Ramsey separated-oscillatory-field method. The information acquired by detecting a sequence of atoms modifies the field step by step, until it eventually collapses into a Fock state. At the same time, the field phase undergoes a diffusive process as a result of the back action of the measurement on the photon-number conjugate variable. Once a Fock state has been generated, its evolution under weak perturbation can be continuously monitored, revealing quantum jumps between various photon numbers. When applied to an initial coherent field, the intermediate steps of the measuring sequence produce quantum superpositions of classical fields, known as ``Schr\"odinger cat states.'' Ways to prepare and detect these states in a cavity subjected to a weak relaxation process are discussed. The effects analyzed in this article could realistically be observed by using circular Rydberg atoms and very high-Q superconducting microwave cavities. The possibility of photon ``manipulation'' through nonresonant atom-field interactions opens a domain in cavity QED studies.
In quantum metrology schemes, one generally needs to prepare mmm copies of NNN entangled particles, such as entangled photon states, and then they are detected in a destructive process to estimate an unknown parameter. Here we present an experimental scheme for estimating this parameter by using repeated indirect quantum nondemolition measurements in the setup consisting of a photon in a superconducting cavity (called a photon box). This interaction-based scheme is able to achieve the phase sensitivity scaling as 1/N1/N1/N with a Fock state of NNN photons. Moreover, we only need to prepare one initial NNN-photon state and it can be used repetitively for mmm trials of measurements. This scheme is shown to sustain the quantum advantage for a much longer time than the damping time of Fock state and be more robust than the common strategy with exotic entangled states. To overcome the $2\ensuremath{\pi}/N$ periodic error in the estimation of the true parameter, we can employ a cascaded strategy by adding a real-time feedback interferometric layout.
An experiment is proposed to visualize stroboscopically in real time the dynamics of a photon oscillating between two cavities. The visualization is implemented by a sequence of weak measurements, which are carried out by probing one of the cavities with a Rydberg atom and detecting a resulting phase shift by Ramsey interferometry. This way to measure the number of photons in a cavity was experimentally realized by Brune et al. [Phys. Rev. Lett. 65, 976, 1990]. We suggest a feedback mechanism which minimizes the disturbance due to the measurement and enables a detection of the original evolution of the radiation field.