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arXiv:quant-ph/0701162

How to check the one-count operator experimentally

Alexandre V. Dodonov, Salomon Sylvain Mizrahi, V. V. Dodonov

Published Jan 22, 2007• 0 citations
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Abstract

We propose an experimental scheme to probe the form of one-count operation used in the theory of continuous photodetection in cavities. Two main steps are: 1) an absorption of a single photon by an atom passing through a high-Q cavity containing electromagnetic field in a thermal or coherent state, 2) a subsequent measurement of the photon statistics in the new field state arising after the photon absorption. Then comparing the probabilities of finding 0 and 1 photons in the initial and final states of the field, one can make conclusions on the form of the one-count operation. This method can be readily applied in the microwave cavity QED with present technology.

DOI
10.48550/arxiv.quant-ph/0701162

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We propose an experimental scheme to probe the form of one-count operation used in the theory of continuous photodetection in cavities. Two main steps are: 1) an absorption of a single photon by an atom passing through a high-Q cavity containing electromagnetic field in a thermal or coherent state, 2) a subsequent measurement of the photon statistics in the new field state arising after the photon absorption. Then comparing the probabilities of finding 0 and 1 photons in the initial and final states of the field, one can make conclusions on the form of the one-count operation. This method can be readily applied in the microwave cavity QED with present technology.
We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ‚Schrödinger cats‘ are among those that may be measured with a two-atom interaction.
Time development of electromagnetic fields in closed cavities under continuous detection of photons continues to be a subject of confusing controversy. Recently Dodonov et al. [Phys. Rev. A, 75, 013806, 2007] argued that their model of quantum superoperators (E model) invalidates some of the predictions of the previously introduced photon counting model of Srinivas and Davies [J. Mod. Optic. 28, 981, 1981] (SD model). Both the SD and the E models are based on two postulated quantum jump superoperators: (1) the one-count operator corresponding to the absorption of a single photon and (2) the no-count operator. In this work we develop a stochastic difference equation that describes the dissipative coupling of the cavity field and the detector. The difference equation is based on non-perturbative treatment of the cavity-detector coupling. In spite of being non-integrable due to the coupling of the detector with an external reservoir it can be used to derive the exact forms of the quantum jump superoperators. When applied to a particular photon counting measurement our theory gives predictions identical with those of the SD model which should be considered a non-perturbative and ab-initio result. It is pointed out that available experimental results coincide with the results given by the ab-initio SD model. We summarize some of the key characteristics of cavity fields and photon counting processes to demonstrate that the results given by the SD model are consistent with the principles of quantum mechanics while those given by the E model are not.
A model for photodetection is presented which permits evolution of the detected field during the detection process. The integrated univariate and bivariate statistics of the photocount are obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation. The scheme encompasses the results of three hitherto disparate photocounting models, and demonstrates explicitly the relation between the univariate photon counting statistics and the photon statistics of the field. First-order photocount correlation functions are derived and compared with the corresponding cavity photon population correlations. Photocount antibunching is examined and found to be possible in this model.
Summary form only given.Decoherence, i.e., the rapid destruction of the phase relation between two quantum states of a system caused by the entanglement of these two states with two different states of the environment, is the main limiting factor for quantum information processing. For this reason, decoherence control is now becoming a rapidly expanding field of investigation. Decoherence control would be particularly useful in high-Q electromagnetic cavities. In fact, one of the few experimental realizations of a quantum gate is the Caltech's quantum phase gate, demonstrating conditional quantum dynamics between polarized modes in a high-finesse optical cavity. Moreover, the progressive decoherence of a mesoscopic Schrodinger cat state has been observed for the first time in the experiment of Brune et al. (1996) where the linear superposition of two coherent states of a field in a microwave cavity, with classically distinct phases, has been generated and detected. Here we propose a photodetection-mediated feedback scheme based on a very simple idea: whenever a photon leaks out from the cavity and is detected by a photodetector, a feedback loop supplies the cavity mode with another photon, using a single ion trapped in the cavity and appropriately shaped laser pulses.
Summary form only given. We have prepared a single-photon entangled state involving two field modes of a high finesse microwave superconducting cavity, and we have probed its coherence after storing it for a variable time in the cavity. We use the resonant interaction between circular Rydberg atoms and the field. This coupling is stronger than any dissipation rate so that the energy exchange between the atoms and the cavity is periodic (Rabi oscillation). A first atom prepares the entangled field state (writer atom) and a second one probes its coherence (reader atom).