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arXiv:1409.0958

Past quantum state analysis of the photon number evolution in a cavity

T. Rybarczyk, Stefan Gerlich, Bruno Peaudecerf, Mariane Penasa, Brian Julsgaard, Klaus Mølmer, S. Gleyzes, M. Brune, J. M. Raimond, S. Haroche, I. Dotsenko

Published Sep 3, 2014• 4 citations
arXivHTMLPDF

Abstract

A quantum system can be monitored through repeated interactions with meters, followed by their detection. The state of the system at time t is thus conditioned on the information obtained until that time. More insight in the state dynamics is provided, however, by the past quantum state (PQS) [S. Gammelmark et al. Phys. Rev. Lett. 111, 160401 (2013)]. It relies on all aspects of the system evolution which are recorded in the past and in the future of t. Using PQS analysis for the quantum non-demolition photon number counting in a cavity, we can reveal information hidden in the standard approach and resolve a wider range of number states. This experiment demonstrates the strong potential of PQS analysis.

DOI
10.48550/arxiv.1409.0958

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A quantum system can be monitored through repeated interactions with meters, followed by their detection. The state of the system at time t is thus conditioned on the information obtained until that time. More insight in the state dynamics is provided, however, by the past quantum state (PQS) [S. Gammelmark et al. Phys. Rev. Lett. 111, 160401 (2013)]. It relies on all aspects of the system evolution which are recorded in the past and in the future of t. Using PQS analysis for the quantum non-demolition photon number counting in a cavity, we can reveal information hidden in the standard approach and resolve a wider range of number states. This experiment demonstrates the strong potential of PQS analysis.
A quantum system can be monitored through repeated interactions with meter systems. The state of the system at time ttt, represented by the density matrix $\ensuremath{\rho}(t)$, then becomes conditioned on the information obtained by the meters until that time. More insight in the state of the system at any time ttt is provided, however, by taking into account the full detection of all meters interacting with the system both in the past and in the future of ttt. We present experiments that use near-resonant atomic probes to monitor the evolution of the quantized field in a cavity. The application of the forward-backward smoothing method to this quantum problem, justified by the past quantum state formalism [S. Gammelmark et al., Phys. Rev. Lett. 111, 160401 (2013)], allows us to resolve a posteriori dynamics, which is not reflected by the usual quantum state $\ensuremath{\rho}(t)$.
The estimation of the state of a quantum system is a central task in quantum information and quantum-enabled metrology. A quantum system can be monitored indirectly through its successive interaction with meters, whose final detection provides information on the system’s state. In the standard, forward, approach, the system’s density operator, ρ, at time t is deduced from all measurements performed up to time t and from our knowledge of the system’s dynamics, including relaxation. The recently introduced past quantum state (PQS) formalism [1] provides us with a simple method to include in the state estimation also information gathered after t. We present here an experiment applying the PQS analysis to a system with a high-dimensional Hilbert space [2].
A microscopic system under continuous observation exhibits at random times sudden jumps between its states. The detection of this essential quantum feature requires a quantum non-demolition (QND) measurement1, 2, 3 repeated many times during the system evolution. Quantum jumps of trapped massive particles (electrons, ions or molecules4,5,6,7,8) have been observed, which is not the case of the jumps of light quanta. Usual photodetectors absorb light and are thus unable to detect the same photon twice. They must be replaced by a transparent counter 'seeing' photons without destroying them3. Moreover, the light has to be stored over a duration much longer than the QND detection time. We have fulfilled these challenging conditions and observed photon number quantum jumps. Microwave photons are stored in a superconducting cavity for times in the second range. They are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms highly correlated in the same state, are interrupted by sudden state-switchings. These telegraphic signals record, for the first time, the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons opens new perspectives for the exploration of the quantum to classical boundary9, 10.
A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t<T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of any measurement at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102, 250403 (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and postselected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A 24, 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes.
Abstract The recent past quantum state formalism (2013 Phys. Rev. Lett. 111, 160401) indicates that the outcome probability of the measurement performed on a quantum system at time t shows dependence on the measurement events recorded until that time, and is also revised by the outcomes acquired after time t. We apply the past quantum state formalism to calculate the three-time correlation function of a radiation field and to analyze the conditional dynamics on the pre- and postselection by the first and last detection events. The persistent oscillations in the three-time field correlation function, which cannot be well understood by the usual quantum regression theorem, are straightforwardly explained by the probabilistic knowledge of the past and the future through the past quantum state reasoning.