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APS

Time evolution of the variance of the field amplitude in cavity QED

Wade P. Smith, G. T. Foster, Joseph E. Reiner, Luis A. Orozco, H. J. Carmichael

Published May 12, 2000• 0 citations
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Abstract

Summary form only given. Reconstruction of quantum states of the electromagnetic field has become an important technique in quantum optics. Tomographic algorithms to reconstruct the Wigner function and direct density matrix measurement schemes both provide a full representation of a quantum state. We are interested in the time evolution of a cavity quantum electrodynamic (QED) system that, after a detected quantum fluctuation, regresses back to its steady state in a dynamical way. We would like to follow the evolution of the state in Hilbert space as it returns back to equilibrium. Few systems in quantum optics have time scales where present day digitizing electronics can capture the signals necessary to reconstruct the state evolution. Our cavity QED system does.

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Summary form only given. Reconstruction of quantum states of the electromagnetic field has become an important technique in quantum optics. Tomographic algorithms to reconstruct the Wigner function and direct density matrix measurement schemes both provide a full representation of a quantum state. We are interested in the time evolution of a cavity quantum electrodynamic (QED) system that, after a detected quantum fluctuation, regresses back to its steady state in a dynamical way. We would like to follow the evolution of the state in Hilbert space as it returns back to equilibrium. Few systems in quantum optics have time scales where present day digitizing electronics can capture the signals necessary to reconstruct the state evolution. Our cavity QED system does.
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.
Summary form only given, as follows. The subject of state reconstruction has recently become a major field of study in quantum optics [see Special issue on Quantum state preparation and measurement, J. Mod Opt., 11/12, (1997), edited by W.P. Schleich and M.G. Raymer]. The quasiprobability functions and density matrices have been measured experimentally for single-mode running fields using the homodyne scheme. However, most of the earlier reconstruction schemes are for single-mode fields. In this presentation the author is interested in reconstruction of a two-mode entangled cavity field.
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.
We report measurements in cavity QED of a wave-particle correlation function which records the conditional time evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical.
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.
The correlation of a photon detection with the record of a homodyne photocurrent has allowed the observation of time-resolved quantum fluctuations of the amplitude of a squeezed electromagnetic wave in a cavity quantum electrodynamic system. The photon detection, through the wavefunction collapse, prepares a conditional state whose evolution back to equilibrium is observed. The perturbation of the wave amplitude is measured at the sub-photon level. The third-order correlation is manifestly non-classical, giving a minimum amplitude at zero delay where there would classically be a maximum; its Fourier transform gives the squeezing spectrum.