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arXiv:0809.1511 · Physical Review Letters

Process Tomography of Field Damping and Measurement of Fock State Lifetimes by Quantum Nondemolition Photon Counting in a Cavity

M. Brune, J. Bernu, Christine Guerlin, S. Deléglise, C. Sayrin, S. Gleyzes, Stefan Kuhr, I. Dotsenko, J. M. Raimond, S. Haroche

Published Dec 8, 2008• 95 citations
arXivHTMLPDF

Abstract

The relaxation of a quantum field stored in a high-Q superconducting cavity is monitored by nonresonant Rydberg atoms. The field, subjected to repetitive quantum nondemolition photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the n photon states (0 < or = n < or = 7) are found to increase linearly with n. The results are in excellent agreement with theory including a small thermal contribution.

DOI
10.1103/physrevlett.101.240402

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The relaxation of a quantum field stored in a high-Q superconducting cavity is monitored by nonresonant Rydberg atoms. The field, subjected to repetitive quantum nondemolition photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the n photon states (0 < or = n < or = 7) are found to increase linearly with n. The results are in excellent agreement with theory including a small thermal contribution.
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We present a method for reconstructing the average evolution of the photon number distribution of a field decaying in a high- Q cavity. It applies an iterative maximum likelihood state reconstruction algorithm to the diagonal elements of the field density operator. It is based on quantum non-demolition measurements carried out with atoms crossing the cavity one by one. A small set of successively detected atoms defines a positive operator valued measure (POVM). The reconstruction is performed by applying this POVM to a large ensemble of field realizations. An optimal POVM based on the detection of a minimal number of atoms is shown to be sufficient to ensure an unambiguous convergence of the reconstruction. The cavity crossing time of this minimal number of atoms must be much shorter than the lifetime of the largest photon number present in the field. We apply the method to monitor the evolution of number states prepared by quantum feedback in a recent experiment. The method could also be useful in circuit QED experiments.
The photon number parity is a binary observable playing an important role in the description of the non-classical features of light. In microwave experiments, this observable can be measured by using a single Rydberg atom evolving in a two dimension space and interacting dispersively with a field stored in one or two cavities. The procedure, based on atomic interferometry, maps the field parity (+ 1 or − 1) onto the states of the two-level atom. By performing repeated measurements of the field parity, it is possible to observe field quantum jumps, to reconstruct the complete Wigner function of an arbitrary field and to study how it evolves due to decoherence.
We propose a quantum nondemolition measurement of the photon-number distribution for a two-mode cavity field. In the scheme two sequences of two-level atoms interact dispersively with the respective cavity modes and resonantly with two classical fields, and then are detected continually. The field finally reduces to a two-mode Fock state. The probability of collapsing to a given Fock state is determined by the initial photon-number distribution. The scheme can be easily generalized to a field with N modes.