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arXiv:1203.0199

Quantum Nondemolition Measurement and Heralded Preparation of Fock States with Electromagnetically Induced Transparency in an Optical Cavity

Guang Lin, Y. P. Niu, Tianyao Huang, X. M. Lin, Wang, Z. Y., Shuang Gong

Published Mar 1, 2012• 0 citations
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Abstract

We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the atomic medium explicitly depends on the number n of photons during the process of transient state dynamics, the measurement on the change of transmission of the probe field can be used for QND measurement of small photon number, and thus create the photon Fock states in particular single-photon state in a heralded way.

DOI
10.48550/arxiv.1203.0199

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We propose a probabilistic scheme to prepare a maximally entangled state between a pair of two-level atoms coupled to a leaking cavity mode in circuit QED, without requiring precise time control of the system evolution and initial atomic state. We show that the steady state of this dissipative system is a mixture of two parts, where the atoms are either in their ground state or in a maximally entangled one. Then, by applying a weak probe field to the cavity mode, we are able to discriminate those states without disturbing the atomic system, i.e., to perform a quantum nondemolition measurement via the cavity transmission. In this scheme, one has maximum cavity transmission only when the atomic system is in an entangled state, so that a single click in the detector is enough to be sure that the atoms are in a maximally entangled state. Our scheme relies on an interference effect as it happens in an electromagnetically induced transparency phenomenon so that it works even in the limit of a cavity decay rate much stronger than the atom-field coupling.
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We propose a scheme for realizing a quantum nondemolition (QND) measurement of a small number of optical photons. Our scheme has two stages: First, we couple a propagating light pulse with fixed photon number to a trapped cold atomic gas within a cavity, such that the pulse is stored within a collective polariton mode. Second, a small-photon-number measurement is engineered by monitoring the cavity-transmission spectrum. Since the polariton mode profile is preserved during the process of detecting the spectrum, photon-number QND measurements could be achieved by retrieving the light pulse from the polariton mode. We also discuss a method which uses QND measurements to generate small-photon Fock states.
Steady-state dynamics of a \ensuremath{\Lambda} atom in a ring cavity driven by two coherent fields are studied for arbitrary detunings, arbitrary incoherent pumping, and coherent driving intensities. Effects of both cavity and effective atom number on electromagnetically induced transparency (EIT) are pointed out. New physical pictures for cavity EIT are given in terms of collective cooperative coefficients and dispersion experienced by the probe. In the regime of smaller collective cooperative coefficients, an absorption-gain profile is reduced to that of a general EIT estimated by the imaginary part of a corresponding dipole moment, and its transparency window is directly proportional to power broadening, if the total Rabi frequency is large enough. But in the region of larger collective cooperative coefficients which means a dense atomic medium, longer optical path, or high-Q cavity, EIT is determined not only by the imaginary part but also by the real part of the corresponding dipole moment, which results in the possibility of observing an EIT central peak with a subnatural width, while there may be nearly no power broadening.