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Quantum Electronics and Laser Science Conference

Conditional evolution in cavity QED

G. T. Foster, D. Greenbaum, Luis A. Orozco

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Summary form only given. The second order intensity correlation function can provide evidence of the non-classical nature of an electric field, as well as information about the dynamics which produce the field. In practice, this is a conditional measurement of the probability to detect a photon given that another photon was detected in coincidence or some time before. We have measured the correlation function of the photons escaping from a strongly coupled cavity QED system consisting of a high finesse interferometer traversed by a beam of optically pumped Rb atoms. In this regime, the rate of reversible exchange of energy between the atoms and the cavity is larger than the cavity decay and spontaneous emission rates, and the saturation photon number is less than one. The correlations exhibit the non-classical features of antibunching and sub-Poissonian statistics, and an oscillation related to the exchange of energy taking place in the coupled system of atoms and cavity field. We view the initial photon detection as causing a projection of the system into a well defined initial state from which it coherently evolves back to steady state. A full characterization of this conditional evolution requires the measurement of the electric field as it evolves from the initial state.

DOI
10.1109/qels.1999.807305

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Summary form only given. The second order intensity correlation function can provide evidence of the non-classical nature of an electric field, as well as information about the dynamics which produce the field. In practice, this is a conditional measurement of the probability to detect a photon given that another photon was detected in coincidence or some time before. We have measured the correlation function of the photons escaping from a strongly coupled cavity QED system consisting of a high finesse interferometer traversed by a beam of optically pumped Rb atoms. In this regime, the rate of reversible exchange of energy between the atoms and the cavity is larger than the cavity decay and spontaneous emission rates, and the saturation photon number is less than one. The correlations exhibit the non-classical features of antibunching and sub-Poissonian statistics, and an oscillation related to the exchange of energy taking place in the coupled system of atoms and cavity field. We view the initial photon detection as causing a projection of the system into a well defined initial state from which it coherently evolves back to steady state. A full characterization of this conditional evolution requires the measurement of the electric field as it evolves from the initial state.
Summary form only given. The second-order correlation function of the intensity is a measurement of the intensity fluctuations and their enhancement or suppression relative to an ideal laser field. It is a sensitive probe of the dynamic processes involved in producing the light. We have measured the correlation function of the photons escaping from a cavity QED system consisting of a high-finesse interferometer traversed by an atomic beam of optically pumped Rb atoms. We observe nonclassical correlations, exhibiting antibunching and sub-Poissonian statistics.
Summary form only given. We have developed a correlation technique that permits us to follow the evolution of the mean amplitude of the conditional electromagnetic field emitted from an optical system. The detection of a photon is correlated with the photocurrent record from a balanced homodyne detector. The measured signal in the homodyne detector is proportional to a correlation between particle wave aspects of light. One application of this technique is the measurement of quadrature amplitude fluctuations which violate classical bounds by orders of magnitude.We use this wave-particle correlator to study the time evolution of the electromagnetic field emitted from a cavity QED system. We operate in the optical regime of cavity QED where a beam of optically pumped two-level Rb atoms traverse the TEM/sub 00/ mode of a high finesse Fabry-Perot cavity.
We report studies of a third-order correlation function that records the conditional time evolution of the field of a fraction of a photon. We present results in the strong-coupling regime of cavity QED, where the detection of a photon from the cavity prepares a state with a well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We perform a homodyne measurement conditioned on the photon detection to observe the regression of the field amplitude. The measured field-photon correlation is nonclassical and can be used to determine the spectrum of squeezing in an efficiency independent way.
Cavity quantum electrodynamics (QED) allows the study of light-matter in-teractions at the most basic level, through precise identification of the coherent and incoherent (dissipative) parts of the system evolution. We present measurements of light from a cavity QED system consisting of a high-finesse optical resonator coupled to a beam of cold Rb atoms. The novelty of the design lies in the interplay of two degenerate and orthogonal polarization modes. One mode (driven) behaves as the canonical cavity mode of the Jaynes-Cummings Hamiltonian, coherently exciting the atoms with a modest coupling strength; the other mode (undriven) collects a small fraction of spontaneously emitted light and provides a probe of the dissipative processes. We first demonstrate the ability to detect individual atoms passing through the cavity modes in real time by coincidence detection of photons from the un-driven mode. Calculation of statistics and correlation functions from the complete photon detection record allows the determination of detection probabilities and the reconstruction of atomic trajectories. We next present evidence of quantum coher-ence that is created, modified, and measured in the excitation-spontaneous emission cycle. The coherence appears as a long-lived quantum beat at the ground-state Larmor frequency, visible in the intensity autocorrelation function of the undriven mode. Quantum jumps of the atomic state, occurring in between the detections of photons from the cavity, result in substantial changes in the frequency and spectral width of the beats. We present the results of a full quantum Monte Carlo calculation in order to quantitatively explain the measurements.
We present the conditional time evolution of the electromagnetic field produced by a cavity QED system in the strongly coupled regime. We obtain the conditional evolution through an intensity–amplitude correlation function that measures the time evolution of the field after the detection of a photon. A connection exists between this correlation function and the spectrum of squeezing, which permits the study of squeezed states in the time domain. We calculate the spectrum of squeezing from the master equation for the reduced density matrix using both the quantum-regression theorem and quantum trajectories. Our calculations not only show that spontaneous emission degrades the squeezing signal, they also point to the dynamical processes that cause this degradation.
Every quantum system subjected to measurements is an open quantum system. The cavity QED system is elegant in that it probes the interaction between two quantum systems, the atom and the field, while its loss mechanisms are well understood and can be externally monitored. The study of cross-correlations in cavity QED is important for understanding how entanglement evolves in open quantum systems. As quantum information science grows we need to learn more about entanglement and how it can be quantified and measured. Correlation functions have been used to compare an electromagnetic field (intensity) of one mode with the electromagnetic field (intensity) of the same mode at a later time or different spatial location. In quantum optics, correlation functions have been calculated and measured to probe the nonclassical field that results from the interaction of a single mode of the electromagnetic field and an ensemble of two-level atoms (the canonical cavity QED system). This field can exhibit antibunching, squeezing, and can violate inequalities required for a classical field. Entanglement in the steady state of a cavity QED system cannot be measured directly with traditional correlation functions (Hanbury-Brown and Twiss type experiments). Cross-correlations, however, interrogate directly both modes of the entangled pair, the transmitted (cavity) and the fluorescent (atom) intensities, and can act as an entanglement witness. This thesis presents the implementation of a cross-correlation measurement in a cavity QED system. The work has required the construction of an apparatus that incorporates laser cooling and trapping with quantum optics to carefully control both the external (center of mass motion) and internal (atomic state) degrees of freedom of a collection of atoms that interact with a single mode of a high finesse Fabry-Perot cavity. We examine theoretically and experimentally a new intensity cross-correlation function which probes the evolution of the cavity field conditioned on the detection of a fluorescent photon from an atom in the cavity. The results open the possibility to generalize the dynamics of entanglement as a physical resource necessary for the nascent quantum information science.