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Acta Sinica Quantum Optica

The Influence of the Cavity Loss on the Regular Pumping Micromaser

TAN WEI-HAN

Published Jan 1, 2004• 0 citations
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Abstract

Basing on the master-equation approach of density matrix, we study the regular pumping one-atom micromaser when the cavity decay is considered during the interaction. By numerical simulation we calculate the threshold satisfied by pumping rate r and damping c, and discuss the influence of cavity loss on the steady photon distribution and the mean photon number.

Related papers

Pump statistics and photon statistics in the micromaser

János A. Bergou, Mark S. Hillery

The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Sub-Poissonian photon statistics in the micromaser

János A. Bergou

The author presents a tutorial review of the quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interaction with the individual reservoirs, i.e. the interactions are uncorrelated. In their approach, which is based on discrete mapping rather than a maser equation, corrections to reservoir theory arise due to correlations between these interactions. The magnitude of these terms is characterized by the quantity p/N ex . Here p, the parameter describing pump beam fluctuations, is the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p<0 to super-Poissonian pump beam fluctuations. N ex is the number of atoms passing through the cavity during the lifetime of the intercavity field. The conventional reservoir limit (standard laser theory) is recovered if p=0 and/or N ex is large. In all other cases the interactions with the gain and loss reservoirs are correlated. The author presents analytical results to demonstrate the effect of pump regularity on steady-state problems (photon statistics, mean number of photons and photon number variance) as well as on transient phenomena (correlation function and spectrum). In particular, it is shown that the approach to equilibrium can have non-Markovian character.

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From sub-Poissonian to super-Poissonian pumping in the micromaser: Corrections to reservoir theory

János A. Bergou, Mark S. Hillery

We present a quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. It handles the interaction with the active atoms (gain) and cavity decay (loss) on an equal footing. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interactions with the individual reservoirs, i.e., the interactions are uncorrelated. In our approach, corrections to reservoir theory arise. They contain the commutator of the gain and loss operators. The magnitude of these additional terms is characterized by the quantity p/${\mathit{N}}_{\mathrm{ex}}$ where p is a parameter describing pump-beam fluctuations. The parameter is, in fact, the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p0 to super-Poissonian pump beam fluctuations. ${\mathit{N}}_{\mathrm{ex}}$ is the number of excited atoms passing through the cavity during the lifetime of the intracavity field. Thus we recover the conventional reservoir limit if p=0 and/or ${\mathit{N}}_{\mathrm{ex}}$ is large. In all other cases the interactions with the gain and loss reservoirs are correlated. We exploit some of the consequences of the additional terms, presenting analytical as well as numerical results for the steady-state photon statistics (mean photon number and photon-number fluctuations, in particular) without resorting to the p expansion.

Physical Review A•Feb 1, 1994•16 citations

Quantum theory of the coherently pumped micromaser: Model and steady-state solution

István Németh, János A. Bergou

A detailed theoretical and experimental study of the atom-field interaction starting from first principles was made possible by the realization of the single-atom micromaser. The situation is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a superconducting cavity. In spite of the considerable amount of work devoted to the study of the micromaser, it still remains to be established how the system behaves under coherent pumping. We present a comprehensive study of the coherently pumped micromaser; we develop an analytic method to obtain the steady-state solution of the master equation governing the time evolution of the cavity field. We illustrate this method with a simple example and present results for the photon distribution and purity of the steady state of the coherently pumped micromaser.

Physical Review A•Aug 26, 2005•2 citations

Micromaser with stationary non-Poissonian pumping

Ulrike Herzog

A method is presented for theoretically investigating the properties of a one-atom micromaser with stationary non-Poissonian pumping. The method is based on treating the statistics of the arrival times of the individual pump atoms with the help of the theory of stochastic point processes. Considerable simplification is achieved by assuming the pump statistics to be described by a stationary renewal process. Thus the influence of super- as well as sub-Poissonian pumping with different strengths of correlation between the pump atoms and different correlation decay times may be studied quantitatively. The level-selective statistics of the atoms leaving the cavity is investigated as well as the photon statistics of the cavity field. Moreover, the relation to the other models used in the literature for describing the micromaser pump statistics is discussed. It is found that for sub- (super-)Poissonian pumping, the stationary expectation value of the cavity photon number (which corresponds to its time-averaged value) is larger (smaller) than the conditioned mean photon number that would result from averaging over the number of photons present in the cavity at the time instants immediately before the injection of the individual pump atoms. For Poissonian pumping, both quantities are shown to be equal. The relative standard deviation of the stationary cavity photon number is decreased (increased) for sub- (super-) Poissonian pumping, in comparison to the corresponding values that would result from Poissonian pumping. Moreover, it turns out that for sub- (super-)Poissonian pumping, the normalized coincidence probability density for the detection of the outgoing deexcited atoms is smaller (larger) than the normalized cavity field intensity correlation function at zero time delay. The difference decreases with increasing lifetime of the pump-atom correlations. Finally, the level-selective delayed coincidence probability densities of the outgoing atoms and their waiting-time distributions are found to be affected greatly by the correlation strength as well as the correlation decay time of the incoming pump atoms.

Physical Review A•Jul 1, 1995•22 citations

One-atom maser with a periodic and noisy pump: An application of damping bases

Hans‐Jürgen Briegel, Berthold‐Georg Englert, Christian Ginzel +1 more

We study the one-atom maser with a periodic-pump scheme for the injected atoms. The dynamics of the system is solved also in a regime where the losses of the field cannot be neglected while the atom is inside the cavity, as is the situation in an optical maser. The time development of the maser field is described by a general evolution operator, whose matrix representation in the damping basis is known analytically for zero temperature. The numerical evaluation of this matrix yields the stationary as well as the transient properties of the maser. Noise-producing mechanisms of the pump are included explicitly in the evolution operator for the field. These are a finite efficiency of the pump laser, a velocity spread in the atomic beam, and spontaneous transitions between the atomic levels and to the ground state. We find that features such as trapped states and sub-Poissonian photon statistics also occur in the high-loss regime like in an optical resonator. The observation of such effects will, as in the ordinary micromaser experiments, depend very sensitively on the reduction of the pump noise. For highly regular excitation, we find a pronounced oscillation of the field-correlation function for a wide range of the transit time, which leads to a distinct line splitting in the spectrum of the field. The amount of the splitting is determined by the periodicity of the pump. For less regular excitation, and in particular in the Poissonian limit, these oscillations disappear.

Physical Review A•Jun 1, 1994•29 citations
Basing on the master-equation approach of density matrix, we study the regular pumping one-atom micromaser when the cavity decay is considered during the interaction. By numerical simulation we calculate the threshold satisfied by pumping rate r and damping c, and discuss the influence of cavity loss on the steady photon distribution and the mean photon number.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.
The author presents a tutorial review of the quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interaction with the individual reservoirs, i.e. the interactions are uncorrelated. In their approach, which is based on discrete mapping rather than a maser equation, corrections to reservoir theory arise due to correlations between these interactions. The magnitude of these terms is characterized by the quantity p/N ex . Here p, the parameter describing pump beam fluctuations, is the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p<0 to super-Poissonian pump beam fluctuations. N ex is the number of atoms passing through the cavity during the lifetime of the intercavity field. The conventional reservoir limit (standard laser theory) is recovered if p=0 and/or N ex is large. In all other cases the interactions with the gain and loss reservoirs are correlated. The author presents analytical results to demonstrate the effect of pump regularity on steady-state problems (photon statistics, mean number of photons and photon number variance) as well as on transient phenomena (correlation function and spectrum). In particular, it is shown that the approach to equilibrium can have non-Markovian character.
We present a quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. It handles the interaction with the active atoms (gain) and cavity decay (loss) on an equal footing. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interactions with the individual reservoirs, i.e., the interactions are uncorrelated. In our approach, corrections to reservoir theory arise. They contain the commutator of the gain and loss operators. The magnitude of these additional terms is characterized by the quantity p/Nex{\mathit{N}}_{\mathrm{ex}}Nex​ where p is a parameter describing pump-beam fluctuations. The parameter is, in fact, the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p0 to super-Poissonian pump beam fluctuations. Nex{\mathit{N}}_{\mathrm{ex}}Nex​ is the number of excited atoms passing through the cavity during the lifetime of the intracavity field. Thus we recover the conventional reservoir limit if p=0 and/or Nex{\mathit{N}}_{\mathrm{ex}}Nex​ is large. In all other cases the interactions with the gain and loss reservoirs are correlated. We exploit some of the consequences of the additional terms, presenting analytical as well as numerical results for the steady-state photon statistics (mean photon number and photon-number fluctuations, in particular) without resorting to the p expansion.
A detailed theoretical and experimental study of the atom-field interaction starting from first principles was made possible by the realization of the single-atom micromaser. The situation is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a superconducting cavity. In spite of the considerable amount of work devoted to the study of the micromaser, it still remains to be established how the system behaves under coherent pumping. We present a comprehensive study of the coherently pumped micromaser; we develop an analytic method to obtain the steady-state solution of the master equation governing the time evolution of the cavity field. We illustrate this method with a simple example and present results for the photon distribution and purity of the steady state of the coherently pumped micromaser.
A method is presented for theoretically investigating the properties of a one-atom micromaser with stationary non-Poissonian pumping. The method is based on treating the statistics of the arrival times of the individual pump atoms with the help of the theory of stochastic point processes. Considerable simplification is achieved by assuming the pump statistics to be described by a stationary renewal process. Thus the influence of super- as well as sub-Poissonian pumping with different strengths of correlation between the pump atoms and different correlation decay times may be studied quantitatively. The level-selective statistics of the atoms leaving the cavity is investigated as well as the photon statistics of the cavity field. Moreover, the relation to the other models used in the literature for describing the micromaser pump statistics is discussed. It is found that for sub- (super-)Poissonian pumping, the stationary expectation value of the cavity photon number (which corresponds to its time-averaged value) is larger (smaller) than the conditioned mean photon number that would result from averaging over the number of photons present in the cavity at the time instants immediately before the injection of the individual pump atoms. For Poissonian pumping, both quantities are shown to be equal. The relative standard deviation of the stationary cavity photon number is decreased (increased) for sub- (super-) Poissonian pumping, in comparison to the corresponding values that would result from Poissonian pumping. Moreover, it turns out that for sub- (super-)Poissonian pumping, the normalized coincidence probability density for the detection of the outgoing deexcited atoms is smaller (larger) than the normalized cavity field intensity correlation function at zero time delay. The difference decreases with increasing lifetime of the pump-atom correlations. Finally, the level-selective delayed coincidence probability densities of the outgoing atoms and their waiting-time distributions are found to be affected greatly by the correlation strength as well as the correlation decay time of the incoming pump atoms.
We study the one-atom maser with a periodic-pump scheme for the injected atoms. The dynamics of the system is solved also in a regime where the losses of the field cannot be neglected while the atom is inside the cavity, as is the situation in an optical maser. The time development of the maser field is described by a general evolution operator, whose matrix representation in the damping basis is known analytically for zero temperature. The numerical evaluation of this matrix yields the stationary as well as the transient properties of the maser. Noise-producing mechanisms of the pump are included explicitly in the evolution operator for the field. These are a finite efficiency of the pump laser, a velocity spread in the atomic beam, and spontaneous transitions between the atomic levels and to the ground state. We find that features such as trapped states and sub-Poissonian photon statistics also occur in the high-loss regime like in an optical resonator. The observation of such effects will, as in the ordinary micromaser experiments, depend very sensitively on the reduction of the pump noise. For highly regular excitation, we find a pronounced oscillation of the field-correlation function for a wide range of the transit time, which leads to a distinct line splitting in the spectrum of the field. The amount of the splitting is determined by the periodicity of the pump. For less regular excitation, and in particular in the Poissonian limit, these oscillations disappear.