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Physical Review A

Strong squeezing in the Jaynes-Cummings model

J. R. Kukliński, J. L. Madajczyk

Published Apr 1, 1988• 220 citations
Publisher

Abstract

Using the well-known solution for a two-level atom interacting with a single mode of radiation (Jaynes-Cummings model), we reanalyze the possibility of squeezing. We found that if only the initial coherent state has a mean photon number exceeding 10 (for a resonant case) significant squeezing can be achieved. Its strength can be arbitrarily large for increasing average photon number. Finally, we solve our model in the situation when the em field is damped and analyze the impact of damping on both squeezing and revival phenomena.

DOI
10.1103/physreva.37.3175

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Physical Review A•Nov 1, 1992•4 citations
Using the well-known solution for a two-level atom interacting with a single mode of radiation (Jaynes-Cummings model), we reanalyze the possibility of squeezing. We found that if only the initial coherent state has a mean photon number exceeding 10 (for a resonant case) significant squeezing can be achieved. Its strength can be arbitrarily large for increasing average photon number. Finally, we solve our model in the situation when the em field is damped and analyze the impact of damping on both squeezing and revival phenomena.
We use the recently-established asymptotic solution (AS) for large fields to study squeezing in the Jaynes-Cummings model. Arbitrary initial atomic states (including atomic coherence) are considered. We find that most features of squeezing can be understood from the properties of the asymptotic field states, and from the observation, which we establish numerically, that for large fields the interference between the two branches of the wavefunction does not contribute significantly to the squeezing (not even near the revival times, when the two field states being superposed have very nearly the same phase). We obtain a limit on the time over which the field may show any squeezing and find that it scales as the 3/4 power of the number of photons. We also obtain a bound on the maximum achievable squeezing for a given number of photons, which is an improvement over earlier estimates. Finally, we discuss some of the shortcomings of the AS, and in particular the existence of a small ghost peak in the field Q function for initial conditions where the AS predicts a single peak, which is enough to destroy the squeezing for certain times.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
Multiphoton interaction of single-mode squeezed-state light and a two-level atom is considered based on the K-photon Jaynes–Cummings model. Time evolution of quantum fluctuation and photon statistical properties of the initial squeezing light are discussed. It is found that through interaction with a two-level atom, larger squeezing levels cannot be achieved in one-photon or multiphoton processes. For photon antibunching behavior of the light field, it is shown that a smaller initial squeezing level and an appropriately larger coherent part of the initial average photon number of the radiation field favor the generation of this nonclassical behavior, especially in the lower-order interaction processes.
An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.
Squeezing of a coherent light field in a cavity by repeated interaction with atoms is studied in the resonance Jaynes-Cummings model. The least quadrature variance \ensuremath{\delta} is calculated for different values of N (mean photon number), t (interaction interval for each time), and K (number of times of interaction). In the one-photon-transition case, \ensuremath{\delta} could be reduced by this process to a certain extent for suitably chosen t. The squeezing becomes worse if K is too large. \ensuremath{\delta} as a function of t and K (for fixed N) has a minimum, which becomes smaller when N increases. The situation of the two-photon-transition case is similar, the only new feature is that \ensuremath{\delta}(K,t) varies with t periodically when N is large. With a favorably chosen value of t (half of the period), analytical formulas for \ensuremath{\delta}(N,K) are obtained in the large-N approximation. These formulas show definitely, both for atoms initially in the upper or lower level, the least quadrature variance \ensuremath{\delta} goes down when K increases up to a quite large value (for atoms in the upper level it is of order N3/2{\mathit{N}}^{3/2}N3/2, while for atoms in the lower level it is of order N) and the achievable minimum value of ${\mathrm{\ensuremath{\delta}}}^{2}$ is of order 1/ \ensuremath{\surd}N . Moreover, the light fields so obtained are nearly in pure states with minimum uncertainty product ${\mathrm{\ensuremath{\delta}}}_{1}$${\mathrm{\ensuremath{\delta}}}_{2}$=1/4.