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Annual Meeting Optical Society of America

Cat bistability in a coherently driven micromaser

Pierre Meystre, John J. Slosser, Martin Wilkens

Published Jan 1, 1990• 0 citations
Publisher

Abstract

We show that a coherently driven dissipative micromaser may display a new kind of bistability of the cavity field and/or the photon number. The bistability is a direct consequence of the presence of trapping states and the robustness of the related cotangent states against the perturbations caused by the cavity losses. The novel features of the bistability stem from the fact that even in the presence of cavity losses, the stationary state of the maser is close to a macroscopic superposition of number states (Schrödinger's cat) in the bistable regime. With increasing injection rate, the bistable regime of the micromaser is reached by means of a route that resembles a first-order phase transition. Hysteresis and other related irreversible effects are discussed.

DOI
10.1364/oam.1990.fcc3

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Physical Review A•Jan 11, 2002•14 citations
We show that a coherently driven dissipative micromaser may display a new kind of bistability of the cavity field and/or the photon number. The bistability is a direct consequence of the presence of trapping states and the robustness of the related cotangent states against the perturbations caused by the cavity losses. The novel features of the bistability stem from the fact that even in the presence of cavity losses, the stationary state of the maser is close to a macroscopic superposition of number states (Schrödinger's cat) in the bistable regime. With increasing injection rate, the bistable regime of the micromaser is reached by means of a route that resembles a first-order phase transition. Hysteresis and other related irreversible effects are discussed.
This dissertation considers both a lossless and a dissipative micromaser in which a monoenergetic beam of two-level atoms in a coherent superposition of their upper and lower states is injected inside a single mode, high-Q cavity. In the lossless case, we find that under appropriate conditions a field initially in a mixed state will evolve to previously unknown pure states, which we call the tangent and cotangent states. In various limits, these states exhibit interesting properties such as sub-Poissonian photon statistics and squeezing, and most importantly they acquire the characteristics of "macroscopic" quantum superpositions. When dissipation of the cavity mode is incorporated into the model, we find that although the field no longer evolves to a pure state, the mixed steady-state field may still retain the properties of a macroscopic superposition under experimentally realizable damping rates. We then evaluate the experimental conditions necessary for the preparation and detection of such macroscopic superpositions.
Coherent superpositions of quantum states are very sensitive to coupling to the environment. The fluctuations associated with this coupling tend to wash out quantum phases, so that in practice only quantum mixtures are observed at the macroscopic level. This problem has been the object of recent interest in connection with measurement theory (Schrodinger cat). Theoretical predictions indicate that the decay of quantum coherences in the so-called pointer basis is amplified by a factor proportional to a measure of the distance in Hilbert space between the states. Micromasers offer a possible experimental tool to investigate the decay of such coherences. Theoretical studies of a lossless version of the micromaster have shown the existence of trapping states | n q 〉 of the cavity mode. These number states are such that atoms injected in the upper state into the cavity experience a 2qπ interaction with the field. Cavity states of the form | ψ 〉 = Σ q C q | n q 〉 are easily shown to be dynamic steady states of the system. Number states are not a pointer basis for the micromaser, and our theoretical results will evidence the qualitative difference in the nature of coherence decay between this and previously studied cases. Because the decay times of micromaser cavities are typically of the order of hundreds of milliseconds, our results should be amenable to experimental verification.
We study the dynamics of a two-photon micromaser driven by a sequence of polarized Rydberg atoms. If cavity losses are neglected, the density matrix of the cavity mode consists of four dynamically decoupled components. Under appropriate trapping conditions, similar to those for the one-photon micromaser, it evolves to a stationary state. When the bare two-photon frequency cancels the ac Stark shift we cannot satisfy the trapping conditions for odd and even photon number states simultaneously. For specific initial conditions, where either only odd or only even number states are initially populated, we may find, however, stationary states that are pure and that can lead to macroscopic superpositions. These pure states are analogous to the cotangent and tangent states of the one-photon micromaser. When the two atomic levels are in resonance with the bare two-photon transition, trapping conditions for odd and even photon number states can be fulfilled simultaneously. Although the ac Stark shift does not allow for pure stationary states, the stationary state resembles an incoherent superposition of only two pure states, to within a relative deviation of 10-3 off purity.
We describe the dynamics of a micromaser pumped by atoms in superposition states and driven by a resonant coherent field. By a quantum jump approach to the master equation solution, we show how the coherences excited in the cavity mode affect the nonclassical steady-state behaviour of the system, in a way that depends on the relative phase between the polarized atoms and the driving field. Both the mean photon number and the phase of the cavity field can be controlled via the atomic transit time and pump rate, or the driving field intensity. The predicted coherence and phase competition effects can show up in the statistics of the populations of outgoing atoms.
In a micromaser where a classical field strongly drives the atoms while they cross the cavity, remarkable atom–atom correlations show up at steady state, which vanish much faster than dissipative decay. Hence we consider atom pair correlation measurements in which the detection of the first probe atom prepares a mesoscopic superposition state of the cavity field, that entangles with a second probe atom. The conditional probabilities for the latter atomic detection provide a description of the decoherence of the superposition state, occurring in an open system in the presence of pumping, driving, dissipative, and thermal effects. The decoherence rate scales as the squared interaction time, that sets the separation in phase space between the superposition components, whereas the quantum coherence is unaffected by the atomic pumping. Hence we further investigate the system when the cavity is not pumped. Starting the correlation measurements from a thermal state, we can describe the effect of temperature on decoherence. Starting from a vacuum state, the superposition states are maximally separated Schrodinger cat states, whose decoherence can thus be monitored.
We investigate the dynamics of a micromaser continuously driven by a resonant coherent field and pumped by atoms injected in superposition states. We formulate a master equation for the system, and by a Monte Carlo wave-function approach we describe the steady-state behavior as a function of atomic-transit time or driving-field intensity. The combined action of polarized atoms and driving field can lead to enhancement or suppression of coherence in system dynamics, including nonclassical effects such as quadrature squeezing, sub-Poissonian photon statistics, and revival of Rabi oscillations, as well as to shifts of the induced cavity-field phase. These results show the possibility of manipulating both the photon number and the phase of the cavity field.