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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Exact trapping state dynamics for the 85 Rb atom micromaser at very high Q and/or very low T

Amitabh Joshi, A. Kremid, N. Nayak, B. V. Thompson, R. Bullough

Published May 6, 1996• 2 citations
Publisher

Abstract

We have used matrix continued fraction methods pioneered previously, to solve essentially exactly for the dynamics of the one 85Rb atom micromaser. A range of cavity Q values and of average atomic input rates R equals Tp-1 and of atomic interaction times tint is studied. For Tp approximately greater than 200tint the system does evolve to a steady state. And even Q equals 5 multiplied by 1010 and temperature T equals 0.070 degrees K are apparently insufficient to avoid evolution to a steady state with finite variance of the cavity field when tint equals 1.54/44 kHz unless Tp is also substantially reduced. Only in this way are actual trapping state dynamics obtained. The field variance v is not a good diagnostic for observing such trapping state dynamics.

DOI
10.1117/12.239855

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Exact trapping state dynamics for the 85Rb atom micromaser at very high Q and/or very low T

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Matrix continued fraction methods pioneered previously [1–3] are used to solve essentially exactly the dynamics of the one 85Rb atom micromaser. Ranges of cavity Q values, of average atomic input rates R = T p −1 and of atomic interaction times t int are studied with the principal aim of minimizing the cavity field variance v. As expected for T p ≳ 200t int the system does evolve to a steady state with v < 1 and sub-Poissonian photon statistics. But even Q = 5 × 1010 and temperature T = 0·070 K are apparently insufficient conditions for avoiding evolution to a steady state with v < 0 when t int = 1·54/(44 kHz) unless T p is also substantially reduced. Only in this way is actual trapping state dynamics obtained for this value of t int, while no example is found where the system evolves to v = 0 and a single Fock state is produced. The field variance v considered alone is not a good diagnostic for observing such trapping state dynamics and more information will be needed in order to describe adequately the cavity field.

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Physical Review A•Aug 1, 1999•14 citations
We have used matrix continued fraction methods pioneered previously, to solve essentially exactly for the dynamics of the one 85Rb atom micromaser. A range of cavity Q values and of average atomic input rates R equals Tp-1 and of atomic interaction times tint is studied. For Tp approximately greater than 200tint the system does evolve to a steady state. And even Q equals 5 multiplied by 1010 and temperature T equals 0.070 degrees K are apparently insufficient to avoid evolution to a steady state with finite variance of the cavity field when tint equals 1.54/44 kHz unless Tp is also substantially reduced. Only in this way are actual trapping state dynamics obtained. The field variance v is not a good diagnostic for observing such trapping state dynamics.
Matrix continued fraction methods pioneered previously [1–3] are used to solve essentially exactly the dynamics of the one 85Rb atom micromaser. Ranges of cavity Q values, of average atomic input rates R = T p −1 and of atomic interaction times t int are studied with the principal aim of minimizing the cavity field variance v. As expected for T p ≳ 200t int the system does evolve to a steady state with v < 1 and sub-Poissonian photon statistics. But even Q = 5 × 1010 and temperature T = 0·070 K are apparently insufficient conditions for avoiding evolution to a steady state with v < 0 when t int = 1·54/(44 kHz) unless T p is also substantially reduced. Only in this way is actual trapping state dynamics obtained for this value of t int, while no example is found where the system evolves to v = 0 and a single Fock state is produced. The field variance v considered alone is not a good diagnostic for observing such trapping state dynamics and more information will be needed in order to describe adequately the cavity field.
Matrix continued fraction methods pioneered previously [1–3] are used to solve essentially exactly the dynamics of the one 85Rb atom micromaser. Ranges of cavity Q values, of average atomic input rates R = T p −1 and of atomic interaction times t int are studied with the principal aim of minimizing the cavity field variance v. As expected for T p ≳ 200t int the system does evolve to a steady state with v < 1 and sub-Poissonian photon statistics. But even Q = 5 × 1010 and temperature T = 0·070 K are apparently insufficient conditions for avoiding evolution to a steady state with v < 0 when t int = 1·54/(44 kHz) unless T p is also substantially reduced. Only in this way is actual trapping state dynamics obtained for this value of t int, while no example is found where the system evolves to v = 0 and a single Fock state is produced. The field variance v considered alone is not a good diagnostic for observing such trapping state dynamics and more information will be needed in order to describe adequately the cavity field.
We report a numerical simulation of the action of the one 85 Rb atom micromaser which shows that the micromaser field evolves towards a steady state equilibrium when the condition that Tp t int satisfies. In this steady state regime the cavity field reaches a steady state after a sufficient number of atoms have passed through the cavity. The cavity temperature T and the cavity quality factor Q can produce a quantitive change when one of them or the two are changed but they are not responsible for the qualitative changes in the micromaser field. Evidently the only responsible parameter for these qualitative changes is the repetition time T p namely if T p t int then the micromaser field evolution is towards a steady state equilibrium. In contrast when T p reduced to the order of t int then the micromaser field evolution is controlled by the trapping state dynamics – no steady state is apparent in this case. The first going-up trapping state at n=3 plays a significant role in the early dynamics of the micromaser field. Moreover the state of the field ultimately evolves towards a mixed state rather than a pure state.
Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.
We study the dynamics of a micromaser where the pumping atoms are strongly driven by a resonant classical field during their transit through the cavity mode. We derive a master equation for this strongly driven micromaser, involving the contributions of the unitary atom-field interactions and the dissipative effects of a thermal bath. We find analytical solutions for the temporal evolution and the steady state of this system by means of phase-space techniques, providing an unusual solvable model of an open quantum system, including pumping and decoherence. We derive closed expressions for all relevant expectation values, describing the statistics of the cavity field and the detected atomic levels. The transient regime shows the buildup of mixtures of mesoscopic fields evolving towards a super-Poissonian steady-state field that, nevertheless, yields atomic correlations that exhibit stronger nonclassical features than the conventional micromaser.
By applying a quantum-trajectory approach to a master equation for the cavity mode density operator, we investigate the dynamics and the trapping states of a micromaser or microlaser including the effects of cavity temperature, two-atom events, atomic velocity spread, and partial excitation of the atomic beam. In the description of two-atom collective effects we allow for the nonsimultaneous arrival of atoms in the cavity, generalizing to a mean number of atoms ${N}_{\mathrm{at}}\ensuremath{\approx}1,$ a recent treatment [M. I. Kolobov and F. Haake, Phys. Rev. A 55, 3033 (1997)]. We show that, in trapping regions, our treatment of two-atom events can give strikingly different effects with respect to the approximation of simultaneous arrival of atom pairs; e.g., detrapping instead of trapping, different times of approach to the steady state, and different photonstatistics. Also, we simulate micromaser dynamics with parameter values corresponding to the recent experimental observation of the trapping effect by Walther and collaborators [H. Weidinger et al., Technical Digest of the European Quantum Electronics Conference '98 (IEEE, Piscataway, NJ, 1998)].