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

Deep squeezing of coherent light in Jaynes-Cummings model

Chang-qi Cao, Ding Xiao-hong

Published Oct 28, 1992• 0 citations
Publisher

Abstract

First, the effect of detuning on squeezing of coherent light is studied by Jaynes-Cummings model in a large N (initial mean photon number) limit. Analytical formulae for quadrature variances are obtained both in one-photon and two-photon transition cases. These formulae show that the effect is quite different in these two cases. In addition, explicit expressions for the k-th minimum of the suppressed variance are given when k is fairly large, which obviously shows it tends to zero according to 1/k2. Second, squeezing of coherent light field in a cavity by repeated interaction with atoms is studied. Numerical calculation shows the variance (delta) can be reduced by this process to a certain extent for suitably chosen interaction time t. But the squeezing becomes worse if the number of times K is too large. In the two-photon transition case, with a favorably chosen value of t, analytical formulae for (delta) (N, K) are obtained in large N approximation. These formulae show definitely that the least variance (delta) goes down when K increases up to quite a large value, and the achievable minimum value of (delta) 2 is in the order of 1/N1/2. Besides, the light field so obtained is nearly in a pure state with a minimum uncertainty product (delta) 1(delta) 2 equals 1/4.

DOI
10.1117/12.140323

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Acta Physica Sinica•Jan 1, 1992•0 citations
First, the effect of detuning on squeezing of coherent light is studied by Jaynes-Cummings model in a large N (initial mean photon number) limit. Analytical formulae for quadrature variances are obtained both in one-photon and two-photon transition cases. These formulae show that the effect is quite different in these two cases. In addition, explicit expressions for the k-th minimum of the suppressed variance are given when k is fairly large, which obviously shows it tends to zero according to 1/k2. Second, squeezing of coherent light field in a cavity by repeated interaction with atoms is studied. Numerical calculation shows the variance (delta) can be reduced by this process to a certain extent for suitably chosen interaction time t. But the squeezing becomes worse if the number of times K is too large. In the two-photon transition case, with a favorably chosen value of t, analytical formulae for (delta) (N, K) are obtained in large N approximation. These formulae show definitely that the least variance (delta) goes down when K increases up to quite a large value, and the achievable minimum value of (delta) 2 is in the order of 1/N1/2. Besides, the light field so obtained is nearly in a pure state with a minimum uncertainty product (delta) 1(delta) 2 equals 1/4.
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.
The effect of detuning on squeezing of coherent light is studied in the Jaynes-Cummings model and in the large-N (mean photon number) limit. Analytical formulas for quadrature variances are obtained both in the one-photon and two-photon transition cases. In the former case, small detuning only has a small (unfavorable) effect on squeezing. In the latter case, however, the effect of detuning is significant. No squeezing will occur at resonance, and by the presence of detuning, there will be a series of minima appearing in the suppressed quadrature variance during time evolution as happens in the one-photon transition case, with the limit of this series tending to zero. The explicit expressions for the kth minima are also given for fairly large k.
The long-time behavior of squeezing of intense coherent light is studied with off-resonance Jaynes-Cummings model. The interaction between field and atom includes both one-photon transition type and two-photon transition type. The analytical formulae for quadrature variances are obtained. In one-photon transition case, small detuning only has small effect on squeezing. For two-photon transition, however, the situation is quite different. No squeezing will occur in resonance case. Only detuning can cause squeezing. Then a series of minimum appear in the suppressed quadrature variance during time evolution. In Urge N limit this se-ries tends to zero.
The long-time behavior of squeezing of intense coherent light is studied with off-resonance Jaynes-Cummings model. The interaction between field and atom includes both one-photon transition type and two-photon transition type. The analytical formulae for quadrature variances are obtained. In one-photon transition case, small detuning only has small effect on squeezing. For two-photon transition, however, the situation is quite different. No squeezing will occur in resonance case. Only detuning can cause squeezing. Then a series of minimum appear in the suppressed quadrature variance during time evolution. In Urge N limit this se-ries tends to zero.
In this paper we have investigated the amplitude squeezing of the intensity-dependent Jayne-Cummings model. An analytic function has been obtained for large [nbar] (mean photon number) to express the light squeezing. We found that the detuning Δ has a favourable effect on the squeezed state. Slightly increasing the detuning can significantly increase the degree of squeezing. The most striking result is that the field can stay in a deep-squeezed state for a long time when Δ/[nbar] is large. Also, for some ranges of the detuning, the maximum squeezing of the field almost does not vary with the change in detuning.
Two level atoms are injected into ideal cavity one by one to interact with the light field therein which intially is in coherent state. In one-photon transition case, the quadrature variance could be reduced by this means for suitably chosen interaction time t. But there exists some limitation, the squeezing will become worse if the number of times K is too large. In twophoton transition case, for large mean photon tumber N and optimum interaction time t = π/ g2, analytical formula for dependence of quadrature variance on N and K can be obtained. This formula shows that deep squeezing can be achieved by suitably chosen K. And the larger the N is, the stronger the achievable squeezing will be.