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European Quantum Electronics Conference (EQEC)

CLEO®/Europe-IQEC 2015, One Page Summary Template Quantum state control with atoms and cavities

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

Published Jun 21, 2015• 0 citations
OpenAlex

Abstract

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].

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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 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.
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 $\ensuremath{\rho}(t)$.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133{}^{133}133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4F=3 \oplus F=4F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133{}^{133}133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4F=3 \oplus F=4F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
Cavity quantum electrodynamics (QED) in the strong-coupling regime provides the opportunity to monitor and control the dynamics of a simple quantum system. A single Cesium atom interacts strongly with single-photon fields in the mode of a high-finesse optical cavity. When the resulting coherent coupling rate dominates dissipation in the system, strong coupling is realized and the system displays distinctively quantum behavior. The coupling between atomic internal states and the quantized cavity field allows for diverse protocols in quantum state preparation, quantum communication, and quantum logic. However, the atom's external or motional state must also be taken into account. My research develops cavity QED in the limit where the coherent atom-field coupling dominates the atomic kinetic energy and thus significantly affects the atomic center-of-mass motion. In this regime, the interaction of the atom with the cavity field provides both a means of controlling atomic motion and a signal for detecting that motion in real time with high signal-to-noise. The sensing capability of the ``atom-cavity microscope" is exploited to trap single atoms with single-photon fields and to monitor their orbits in real time as they are bound in the cavity. Such real-time position sensing is the basis for a detailed strategy and ongoing experiment to actively stabilize select aspects of an atom's motion within the cavity. As the cavity-enabled position measurement approaches the standard quantum limit, this work begins to realize a quantum servo for atomic position and to address questions of optimal state estimation and state preparation. In combination with other progress in cavity QED, it furthers the goal of controlled atom-field interactions for quantum information science.