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Physical Review A

Time-dependent electric field fluctuations at the subphoton level

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

Published Sep 16, 2002• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.66.033807

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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.
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.
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.
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.
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 intensity-amplitude correlation functions for a driven cavity QED system with two non-identical atoms are investigated in this paper. With the support of conditional homodyne detection, one can detect the time-dependent intensity-amplitude correlation functions experimentally. We find time-asymmetry in this correlation when the driving field is tuned to be resonant with the two-photon excitation state, which brings non-Gaussian fluctuations. The physical origin of these phenomena is the distinction of the third-order moment based on complete-collapse and partial-collapse, which corresponds to the measuring sequence of the intensity and amplitude. Finally, we also examined the nonclassical features of the system, which always exhibits photon bunching. The squeezing occurs in the region of weak driving and disappears with the increase of driving strength. Hence, a new classical inequality based on the technique of homodyne cross-correlation measurement is introduced to determine the nonclassicality of the non-Gaussian system in the region of unsqueezing.
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.