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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Amplitude squeezing of coherent light in a high-Q cavity by regular injection of atoms of two-photon transition

Chang-qi Cao

Published Dec 1, 1995• 1 citation
Publisher

Abstract

The amplitude squeezing of coherent light in a high-Q cavity by interaction with atoms entering regularly one by one is studied. The interaction is assumed to be of two-photon transition type, and the mean photon number N of the initial coherent light is assumed to be large. The interaction interval tau for an individual atom is taken as the favourable value pi /g, where g denotes the effective coupling constant. This value makes an incoming atom in the upper level change to the lower level at the exit. The Golubev-Sokolov equation for the density matrix of photons and generating function approach are utilized without any approximation. From this equation, the variance squared of photon number av as a function of t is derived. Over a certain range of parameters, av/ av may have a minimum value much lower than its steady-state value 1/2 at some moment. The correlation functions and power spectrums of the photon number noise and of the output photon current noise are also investigated.

DOI
10.1088/1355-5111/7/6/001

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Acta Physica Sinica•Jan 1, 1992•0 citations
The amplitude squeezing of coherent light in a high-Q cavity by interaction with atoms entering regularly one by one is studied. The interaction is assumed to be of two-photon transition type, and the mean photon number N of the initial coherent light is assumed to be large. The interaction interval tau for an individual atom is taken as the favourable value pi /g, where g denotes the effective coupling constant. This value makes an incoming atom in the upper level change to the lower level at the exit. The Golubev-Sokolov equation for the density matrix of photons and generating function approach are utilized without any approximation. From this equation, the variance squared of photon number av as a function of t is derived. Over a certain range of parameters, av/ av may have a minimum value much lower than its steady-state value 1/2 at some moment. The correlation functions and power spectrums of the photon number noise and of the output photon current noise are also investigated.
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.
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.
The statistical and squeezing properties of the cavity light produced by a three-level laser are studied. In the laser, N three-level atoms in an open cavity are coupled with a two-mode vacuum reservoir and are pumped to the top level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have obtained the global and local photon statistics for single-mode cavity light beams and for two-mode cavity light. It is found that the global mean photon number and the global photon-number variance of the light emitted from the top are greater than those for the light emitted from intermediate level. The cavity lights emitted from the top and intermediate levels can be separately in a chaotic state under certain conditions. However, the two-mode cavity light is in a squeezed state under certain conditions. We have established that the maximum quadrature squeezing of the two-mode cavity light to be about 46% below the coherent-state level. The presence of the vacuum reservoir noise has the effect of increasing the photon-number variance and decreasing the quadrature squeezing of the cavity light but has no effect on the mean photon number. We have shown that the local mean photon number and photon number variance of the cavity light approach the global mean photon number and photon number variance of the cavity light as the frequency interval increases.
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.