The realization of the micromaser prompted theoretical interest in the fundamental problems of la... more The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.
Time evolution in textbook quantum mechanics is represented by unitary maps \(\vert \psi \rangle ... more Time evolution in textbook quantum mechanics is represented by unitary maps \(\vert \psi \rangle \rightarrow U\vert \psi \rangle\) and \(\rho \rightarrow U\rho {U}^{\dag }\), where \(U ={ \mathrm{e}}^{-itH}\). This is not the most general evolution possible. We can couple our system to another one, evolve both with a unitary operator that will, in general, create entanglement between the two systems, and then trace out the second system. The resulting evolution for the original system alone will be non-unitary, in general, and can be described by a non-unitary quantum map.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number d... more 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.
As originally conceived a correlated spontaneous emission laser showed quenching of spontaneous e... more As originally conceived a correlated spontaneous emission laser showed quenching of spontaneous emission quantum fluctuations in the relative phase angle of a two mode laser. It has been shown by several approaches (e.g. quantum noise operator, Fokker-Planck equation, etc.) that such devices can, in principle, have vanishing noise in this relative phase angle. A geometric pictorial analysis along these lines has been given and provides a simple intuitive explanation for this quantum noise quenching which has also been supported by recent experimental investigations.
We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injec... more We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injected atomic coherences. The lower two levels are coupled by an external classical field. The master equation and the Fokker–Planck equation are derived. Phases of the two modes are locked to a value depending on the phase of the external field, the phase of the injected coherence and the population of the lower two levels. Lasing without inversion and without threshold is found for both modes with and without injected coherences. Applying the appropriate initial atomic coherences one can switch intensities between the two modes, as well as bifurcation and multiple branching can be found when coherences among all levels are present. It is also possible to find phase bistability at a fixed intensity for one of the two modes, when high pump is applied. Strong intensity and phase noise reduction can be found in one of the modes at the expense of increased noises in the other one. Near Poisson...
Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, 1995
ABSTRACT The authors demonstrate the effect of atomic coherence on the generic example of two los... more ABSTRACT The authors demonstrate the effect of atomic coherence on the generic example of two lossless micromasers coupled in series by a common pump beam of excited two-level atoms. The fields are studied via conditional measurements on the final state of the atoms. They consider the two simplest sequences: in the energy preserving (transferring) scheme they require each atom to be detected in its upper (lower) state. Due to the two paths that the atoms can follow to reach the same final state correlation between the two macroscopically separated fields can arise. The authors discuss a scheme which leads to the generation of entangled trapping states of the two fields of the form, mod n,n+M)+or- mod n+M,n), starting from number states mod n, n). Starting from initial coherent states arbitrary steady-state superpositions of the two fields can be generated by switching from the energy transferring to the preserving scheme at an optimum number of atoms. In the absence of dissipations, both methods can produce steady-state coherent superpositions of arbitrary number states of two macroscopically separated fields (nonlocal 'Schrodinger-cats'). A scheme is discussed where entanglement can be transferred from the fields to two atomic beams. Finally, the authors briefly discuss the effect of injected atomic coherence on lasers.
The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantit... more The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2....
The realization of the micromaser prompted theoretical interest in the fundamental problems of la... more The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.
Time evolution in textbook quantum mechanics is represented by unitary maps \(\vert \psi \rangle ... more Time evolution in textbook quantum mechanics is represented by unitary maps \(\vert \psi \rangle \rightarrow U\vert \psi \rangle\) and \(\rho \rightarrow U\rho {U}^{\dag }\), where \(U ={ \mathrm{e}}^{-itH}\). This is not the most general evolution possible. We can couple our system to another one, evolve both with a unitary operator that will, in general, create entanglement between the two systems, and then trace out the second system. The resulting evolution for the original system alone will be non-unitary, in general, and can be described by a non-unitary quantum map.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number d... more 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.
As originally conceived a correlated spontaneous emission laser showed quenching of spontaneous e... more As originally conceived a correlated spontaneous emission laser showed quenching of spontaneous emission quantum fluctuations in the relative phase angle of a two mode laser. It has been shown by several approaches (e.g. quantum noise operator, Fokker-Planck equation, etc.) that such devices can, in principle, have vanishing noise in this relative phase angle. A geometric pictorial analysis along these lines has been given and provides a simple intuitive explanation for this quantum noise quenching which has also been supported by recent experimental investigations.
We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injec... more We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injected atomic coherences. The lower two levels are coupled by an external classical field. The master equation and the Fokker–Planck equation are derived. Phases of the two modes are locked to a value depending on the phase of the external field, the phase of the injected coherence and the population of the lower two levels. Lasing without inversion and without threshold is found for both modes with and without injected coherences. Applying the appropriate initial atomic coherences one can switch intensities between the two modes, as well as bifurcation and multiple branching can be found when coherences among all levels are present. It is also possible to find phase bistability at a fixed intensity for one of the two modes, when high pump is applied. Strong intensity and phase noise reduction can be found in one of the modes at the expense of increased noises in the other one. Near Poisson...
Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, 1995
ABSTRACT The authors demonstrate the effect of atomic coherence on the generic example of two los... more ABSTRACT The authors demonstrate the effect of atomic coherence on the generic example of two lossless micromasers coupled in series by a common pump beam of excited two-level atoms. The fields are studied via conditional measurements on the final state of the atoms. They consider the two simplest sequences: in the energy preserving (transferring) scheme they require each atom to be detected in its upper (lower) state. Due to the two paths that the atoms can follow to reach the same final state correlation between the two macroscopically separated fields can arise. The authors discuss a scheme which leads to the generation of entangled trapping states of the two fields of the form, mod n,n+M)+or- mod n+M,n), starting from number states mod n, n). Starting from initial coherent states arbitrary steady-state superpositions of the two fields can be generated by switching from the energy transferring to the preserving scheme at an optimum number of atoms. In the absence of dissipations, both methods can produce steady-state coherent superpositions of arbitrary number states of two macroscopically separated fields (nonlocal 'Schrodinger-cats'). A scheme is discussed where entanglement can be transferred from the fields to two atomic beams. Finally, the authors briefly discuss the effect of injected atomic coherence on lasers.
The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantit... more The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2....
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Papers by János Bergou