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Physical Review A

Phase-sensitive population decay: The two-atom Dicke model in a broadband squeezed vacuum

G. Massimo Palma, P. L. Knight

Published Feb 1, 1989• 112 citations
Publisher

Abstract

We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.

DOI
10.1103/physreva.39.1962

Related papers

Comment on ‘‘Phase-sensitive population decay: The two-atom Dicke model in a broadband squeezed vacuum’’

Z. Ficek, P. D. Drummond

A recent paper [G. M. Palma and P. L. Knight, Phys. Rev. A 39, 1962 (1989)] has stated that the two-atom Dicke model exhibits phase-dependent population decay. In this Comment we show that population decay is invariant with respect to the input phase angle of squeezing in the two-atom Dicke model.

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Three-level atoms in phase-sensitive broadband correlated reservoirs

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A three-level atom with two competing transitions can sense correlations between modes of an electromagnetic field with which it interacts. We examine the sensitivity of three-level atoms in ladder, \ensuremath{\Lambda}, and V configurations to correlations between modes in a broadband correlated reservoir of field modes. Our model of a correlated reservoir includes pairwise mode correlations around a center frequency. When such correlations are set to zero, the reservoir becomes a simple thermal heat bath, but in the opposite extreme when the modes are perfectly correlated, we recover a minimum-uncertainty broadband squeezed vacuum. We show that atomic populations are extremely sensitive to these correlations, and can, in the ladder system, become inverted as a result of the phase-sensitive noise. We also show how atomic population trapping is affected by mode correlations.

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Establishment of correlated pure states through decay in a squeezed reservoir

ARTUR K. EKERT, G. Massimo Palma, Stephen Mark Barnett +1 more

Our normal understanding of the dissipative relaxation of a quantum system interacting with a reservoir or heat bath leads us to expect that the final state of the quantum system is a mixed state characteristic of one subsystem in equilibrium with the larger reservoir. We show that the broadband squeezed vacuum has such strong correlations in its quantum noise that, although it represents a true reservoir, the decay of subsystems, such as pairs of atoms or oscillators interacting with a squeezed reservoir, relaxes to a pure state that reflects these strong correlations.

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Reply to ‘‘Comment on ‘Phase-sensitive population decay: The two-atom Dicke model in a broadband squeezed vacuum’ ’’

G. Massimo Palma, P. L. Knight

We clarify the nature of phase sensitivity in atomic decay in a broadband squeezed light field.Received 1 February 1990DOI:https://doi.org/10.1103/PhysRevA.42.1829©1990 American Physical Society

Physical Review A•Aug 1, 1990•2 citations

Spontaneous emission from two atoms interacting with a broadband squeezed vacuum

Z. Ficek

Spontaneous emission from two-level atoms interacting with a squeezed vacuum field is examined, taking account of possible different interatomic separations. It is shown that the steady-state atomic population depends on whether the interatomic separations are comparable to or much smaller than the resonant wavelength. For the extended system the squeezed vacuum introduces a dependence of the atomic population on the interatomic separations. For large interatomic separations the atomic population is identical to that for the thermal field, which is the same for two independent atoms. For small interatomic separations the atomic population is higher than that for the thermal field. This is in contrast to the small-sample model in which the interatomic separation is ignored. In this case the final atomic population in the squeezed vacuum is the same as that for the independent atoms in the squeezed vacuum. Moreover, this population differs from that for the thermal field for which the atomic population is lower than that for the independent atoms. This difference is due to the interatomic correlations whose presence depends on whether the interatomic separation is or is not included. For the extended system the interatomic correlations are induced by the squeezed field and vanish for the thermal field. For the small-sample model, however, the interatomic correlations are induced by the thermal field and the squeezed vacuum changes these correlations in such a way that for the minimum-uncertainty squeezed states these correlations vanish. We also discuss the effect of the interatomic separation on the two-photon transitions and the normalized intensity correlation function in the two-atom system interacting with the squeezed vacuum field.

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Canonical transformation and decay into phase-sensitive reservoirs

ARTUR K. EKERT, P. L. Knight

We show that the master equation describing the dissipative evolution of a bosonic quantum system coupled to a phase-sensitive reservoir may be reduced to a standard form of dissipation for a thermal reservoir by canonical transformations. The solution to the master equation for complex phase-sensitive interaction induced, for example, by broadband squeezed light, may then be obtained by a transformation from the known solutions for the simpler thermal case. We show that canonical transformations have a particularly useful form when describing the evolution of quantum dissipative systems in phase space using the Wigner function. We illustrate these ideas with two phase-sensitive dissipative problems: that of the correlated-emission laser and of decay induced by a broadband squeezed vacuum field.

Physical Review A•Jul 1, 1990•51 citations
We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.
A three-level atom with two competing transitions can sense correlations between modes of an electromagnetic field with which it interacts. We examine the sensitivity of three-level atoms in ladder, \ensuremath{\Lambda}, and V configurations to correlations between modes in a broadband correlated reservoir of field modes. Our model of a correlated reservoir includes pairwise mode correlations around a center frequency. When such correlations are set to zero, the reservoir becomes a simple thermal heat bath, but in the opposite extreme when the modes are perfectly correlated, we recover a minimum-uncertainty broadband squeezed vacuum. We show that atomic populations are extremely sensitive to these correlations, and can, in the ladder system, become inverted as a result of the phase-sensitive noise. We also show how atomic population trapping is affected by mode correlations.
Our normal understanding of the dissipative relaxation of a quantum system interacting with a reservoir or heat bath leads us to expect that the final state of the quantum system is a mixed state characteristic of one subsystem in equilibrium with the larger reservoir. We show that the broadband squeezed vacuum has such strong correlations in its quantum noise that, although it represents a true reservoir, the decay of subsystems, such as pairs of atoms or oscillators interacting with a squeezed reservoir, relaxes to a pure state that reflects these strong correlations.
Spontaneous emission from two-level atoms interacting with a squeezed vacuum field is examined, taking account of possible different interatomic separations. It is shown that the steady-state atomic population depends on whether the interatomic separations are comparable to or much smaller than the resonant wavelength. For the extended system the squeezed vacuum introduces a dependence of the atomic population on the interatomic separations. For large interatomic separations the atomic population is identical to that for the thermal field, which is the same for two independent atoms. For small interatomic separations the atomic population is higher than that for the thermal field. This is in contrast to the small-sample model in which the interatomic separation is ignored. In this case the final atomic population in the squeezed vacuum is the same as that for the independent atoms in the squeezed vacuum. Moreover, this population differs from that for the thermal field for which the atomic population is lower than that for the independent atoms. This difference is due to the interatomic correlations whose presence depends on whether the interatomic separation is or is not included. For the extended system the interatomic correlations are induced by the squeezed field and vanish for the thermal field. For the small-sample model, however, the interatomic correlations are induced by the thermal field and the squeezed vacuum changes these correlations in such a way that for the minimum-uncertainty squeezed states these correlations vanish. We also discuss the effect of the interatomic separation on the two-photon transitions and the normalized intensity correlation function in the two-atom system interacting with the squeezed vacuum field.
We show that the master equation describing the dissipative evolution of a bosonic quantum system coupled to a phase-sensitive reservoir may be reduced to a standard form of dissipation for a thermal reservoir by canonical transformations. The solution to the master equation for complex phase-sensitive interaction induced, for example, by broadband squeezed light, may then be obtained by a transformation from the known solutions for the simpler thermal case. We show that canonical transformations have a particularly useful form when describing the evolution of quantum dissipative systems in phase space using the Wigner function. We illustrate these ideas with two phase-sensitive dissipative problems: that of the correlated-emission laser and of decay induced by a broadband squeezed vacuum field.