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Squeezing in resonance fluorescence: effects of atomic localization

R. L. de Matos Filho, W. Vogel

Published May 8, 1994• 0 citations
OpenAlex

Abstract

Squeezing in resonance fluorescence was predicted more than a decade ago,1 but it has not been observed until now. There are lwo problems in connection with such an experiment. First, in a homodyne measurement of the photon statistics the observable effect is limited by the detection and collection efficiencies and is therefore extremely small.2 Second, since the squeezing effect is phase sensitive, the atom must be localized very well. To overcome these problems, homodyne intensity-correlation measurements of the fluorescence from a trapped ion have been proposede.3

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Squeezing and anomalous moments in resonance fluorescence

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A scheme for measuring squeezing in resonance fluorescence from a single trapped and cooled ion is proposed, which is based on the observation of photon pair correlations after beating the fluorescence with a local oscillator. In addition to squeezing, anomalous moments and sub-Poissoinian photon statistics of the fluorescence contribute to the nonclasical behavior of the light in homodyne detection.

Physical Review Letters•Oct 28, 1991•76 citations

Photon-counting statistics of squeezed states in collective resonance fluorescence

Z. Ficek, R. Tanaś, S. Kielich

The photon-counting statistics of squeezed states in collective time-dependent resonance fluorescence is calculated for the homodyne detection technique. The secular approximation is applied to obtain analytical expressions for the photon-counting distribution produced by homodyning the fluorescent field and coherent radiation. Squeezing is shown to appear only in the transient regime of resonance fluorescence. The time location of squeezing is independent of the number of atoms, N, but squeezing increases with increasing N. Moreover, squeezing occurs only for a judicious choice of the phase of the local oscillator and occurs over long counting times T. The time interval T is strongly dependent on the initial atomic population. If initially all atoms are in their excited states, squeezing appears with a delay twice as long as that for initially nonexcited atoms.

Journal of Physics D Applied Physics•Oct 14, 1988•1 citation

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Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.

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Phase-sensitive detection of resonance fluorescence, i.e., allowing the light emitted from an atom which is undergoing Rabi oscillations in free space to interfere with a coherent local oscillator (LO) beam, has drawn considerable attention throughout the history of quantum optics. Recently, phase-sensitive squeezing spectra for single-atom resonance fluorescence were observed for the first time using strongly-driven long-lived atoms. A measurement of phase-sensitive intensity correlations for this system will be presented. Using physical arguments I will construct the phase-sensitive two-time intensity autocorrelation function, and elucidate the role played by quantum fluctuations in phase-dependent resonance fluorescence.

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Emergence and degradation of squeezing in resonance fluorescence

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Using master equation and quantum Monte Carlo wavefunction approaches, we study the circumstances surrounding the emergence and degradation of the elusive squeezing of fluctuations in two-level atom resonance fluorescence. For its measurement we suggest conditional homodyne detection (CHD) [G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, H.J. Carmichael, Phys. Rev. Lett. 85, pp. 3149-3152, 2000], which is nearly independent of detector efficiencies, which have harmed previous attemps. Squeezing in resonance fluorescence requires a weak laser, so the average interval between emitted photons is much longer than the regression time to the steady state; here, the spectrum of the out-of-phase quadrature is a negative peak. In CHD, moderate fields generate a non-zero third-order correlation in the dipole fluctuations that contaminates squeezing, making the noise non- Gaussian. If the probability to emit two and even three close photons is still small the additional contribution is also negative, helping to make the full spectrum a bit larger and easier to measure. Strong driving spreads the photoemission distribution, which destroys squeezing, and the third order fluctuations become responsible for the non-classicality of the fluorescence.

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Observation of Squeezing in Free-Space Phase-Dependent Resonance Fluorescence

Zhou Lu, Samir Bali, John E. Thomas

We measure squeezing spectra for phase-dependent fluorescence of coherently driven two-level atoms in free space. The measured spectra are in excellent agreement with our predictions for a single two-level atom. We find that maximum squeezing occurs for homodyne detection at a phase near ±45° relative to the exciting field, rather than in the in- or out-of-phase quadratures. A new physical picture of phase-dependent noise that incorporates quantum collapses into a Bloch vector model shows why this occurs.

Kluwer Academic Publishers eBooks•Dec 19, 2005•1 citation
Squeezing in resonance fluorescence was predicted more than a decade ago,1 but it has not been observed until now. There are lwo problems in connection with such an experiment. First, in a homodyne measurement of the photon statistics the observable effect is limited by the detection and collection efficiencies and is therefore extremely small.2 Second, since the squeezing effect is phase sensitive, the atom must be localized very well. To overcome these problems, homodyne intensity-correlation measurements of the fluorescence from a trapped ion have been proposede.3
The photon-counting statistics of squeezed states in collective time-dependent resonance fluorescence is calculated for the homodyne detection technique. The secular approximation is applied to obtain analytical expressions for the photon-counting distribution produced by homodyning the fluorescent field and coherent radiation. Squeezing is shown to appear only in the transient regime of resonance fluorescence. The time location of squeezing is independent of the number of atoms, N, but squeezing increases with increasing N. Moreover, squeezing occurs only for a judicious choice of the phase of the local oscillator and occurs over long counting times T. The time interval T is strongly dependent on the initial atomic population. If initially all atoms are in their excited states, squeezing appears with a delay twice as long as that for initially nonexcited atoms.
Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.
Phase-sensitive detection of resonance fluorescence, i.e., allowing the light emitted from an atom which is undergoing Rabi oscillations in free space to interfere with a coherent local oscillator (LO) beam, has drawn considerable attention throughout the history of quantum optics. Recently, phase-sensitive squeezing spectra for single-atom resonance fluorescence were observed for the first time using strongly-driven long-lived atoms. A measurement of phase-sensitive intensity correlations for this system will be presented. Using physical arguments I will construct the phase-sensitive two-time intensity autocorrelation function, and elucidate the role played by quantum fluctuations in phase-dependent resonance fluorescence.
Using master equation and quantum Monte Carlo wavefunction approaches, we study the circumstances surrounding the emergence and degradation of the elusive squeezing of fluctuations in two-level atom resonance fluorescence. For its measurement we suggest conditional homodyne detection (CHD) [G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, H.J. Carmichael, Phys. Rev. Lett. 85, pp. 3149-3152, 2000], which is nearly independent of detector efficiencies, which have harmed previous attemps. Squeezing in resonance fluorescence requires a weak laser, so the average interval between emitted photons is much longer than the regression time to the steady state; here, the spectrum of the out-of-phase quadrature is a negative peak. In CHD, moderate fields generate a non-zero third-order correlation in the dipole fluctuations that contaminates squeezing, making the noise non- Gaussian. If the probability to emit two and even three close photons is still small the additional contribution is also negative, helping to make the full spectrum a bit larger and easier to measure. Strong driving spreads the photoemission distribution, which destroys squeezing, and the third order fluctuations become responsible for the non-classicality of the fluorescence.
We measure squeezing spectra for phase-dependent fluorescence of coherently driven two-level atoms in free space. The measured spectra are in excellent agreement with our predictions for a single two-level atom. We find that maximum squeezing occurs for homodyne detection at a phase near ±45° relative to the exciting field, rather than in the in- or out-of-phase quadratures. A new physical picture of phase-dependent noise that incorporates quantum collapses into a Bloch vector model shows why this occurs.