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Acta Physica Sinica

GENERATION OF SQUEEZED LIGHT IN IDEAL CAVITY BY INJECTING ATOMS

Chunyan Cao

Published Jan 1, 1992• 0 citations
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Abstract

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.

Related papers

GENERATION OF SQUEEZED LIGHT IN IDEAL CAVITY BY INJECTING ATOMS

Chang-qi Cao, Ding Xiao-hong, 北京大学物理系,北京100871

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.

Acta Physica Sinica•Jan 1, 1992•0 citations

Squeezing of coherent light by repeated interaction with atoms

Chang-qi Cao, Ding Xiao-hong

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 ${\mathit{N}}^{3/2}$, 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.

Physical Review A•Nov 1, 1992•4 citations

Deep squeezing of coherent light in Jaynes-Cummings model

Chang-qi Cao, Ding Xiao-hong

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 28, 1992•0 citations

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

Chang-qi Cao

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.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Dec 1, 1995•1 citation

A THEORETICAL STUDY OF GENERATION OF A STRONG SQUEEZED CAVITY FIELD BY USE OF ONE PHOTON MICROMASER

LI Fu-li, 兰州大学现代物理系,兰州,730001,西安交通大学物理系,西安,710049

In this paper interaction of two-level atoms initially occupied the upper most level with a single mode of cavity field initially in a coherent state is investigated. Let the atoms interact in sequence with the field in equal time intervals and we find that the field can be kept in squeezed states and squeezed continuously in this process if initial intensity of the field is strong. The atoms interacting with the squeezed light are also discussed.

Acta Physica Sinica•Jan 1, 1990•0 citations

Optimum field squeezing from atomic sources: Three-level atoms

Bryan J. Dalton, Z. Ficek, P. L. Knight

Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, \ensuremath{\Lambda}, and ``ladder'' systems).We show that for V and \ensuremath{\Lambda} systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.

Physical Review A•Sep 1, 1994•24 citations
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.
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.
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 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.
Light emitted from laser-driven atoms often has squeezed quadrature fluctuations reflecting the phase dependence of the atomic source excited into a coherent superposition by the driving field. In this paper, we study the maximum squeezing in the emitted light fields from three-level atoms, paying particular attention to the role of atomic coherences in governing the optimum squeezing which is possible. Some phase dependent nonlinear optical processes have the potential for substantial quantum noise reduction at useful intensities: for example, four-wave mixing involving atomic systems has already been used to generate quadrature-squeezed light. The threoretical description of such a source is generally complicated with damping processes, coherent and incoherent pumping, and so on, all needing to be taken into account. Fully quantum treatments are available, but the basic physics of the process is often difficult to grasp in the necessarily complicated analysis. Although less important from the point of view of efficient practical sources of squeezed light, studying the generation of squeezed light in simpler systems such as two- or three-level atoms interacting with one or two modes (as in Jaynes-Cummings models) or in spontaneous emission or resonance fluorescence gives greater insight into the fundamentals of the squeezing process. In particular, the relationship between the atomic coherences and the degree of squeezing in the generated fields can be explored. We study the maximum (optimized) squeezing that can be obtained in the emitted fields from the irreversible decay from three-level atoms for any choice of initial conditions, excitations and decay process, for all quadrature components and for all possible configurations (V, \ensuremath{\Lambda}, and ``ladder'' systems).We show that for V and \ensuremath{\Lambda} systems, optimum squeezing is actually associated with a two-level state (in a suitable basis) involving a single one-photon coherence, but for ladder systems the state for maximum noise reduction is not equivalent to a two-level system and involves a single two-photon coherence and no intermediate state population. We pay particular attention to whether the total field is in a minimum uncertainty state, and the nature of the atomic state associated with maximum squeezing, especially whether it is a mixed or pure state. In the case where the initial free field has a zero amplitude at the detector and the source atoms are confined to a region small compared to the wavelength (Dicke source) we show that the squeezing in the total field is given in terms of the squeezing in the source field, and hence related to atomic populations and atomic one-photon and two-photon coherences for the case of three level atom. Previously unconsidered source-free field interferences terms are shown to be zero. The choice of quadrature phase and frequency is optimized to minimize the source field normally ordered variance. We then minimize further with respect to the choice of atomic density matrix elements subject to the constraints that the density matrix is Hermitean, positive, and has a trace equal to unity. In all cases we find that the optimum squeezing is produced when the source field is in a minimum uncertainty state.