Photon statistics of the micromaser with a Kerr medium

We have established the master equation for the micromaser with a Kerr medium,we have studied the photon statics of the micromaser with a Kerr medium field and analysed the influence of the Kerr effect on the photon statistics,The influence of the Kerr effect on the photon statistics is different in two regimes,In the thermal-atom regime,the Kerr effect produces quantum noise,and decreases the mean photon number.In the ultracold-atom regime,with the increase of the nonlinear parameter of the Kerr medium,the stability of the mean photon number and the normalized variance enhances the mean photon number,and the normalized variance exhibits collapse-revival phenomena periodically,their resonance peaks become lower,and the photon statistics of more and more regions are sub-Poissonian.     

Phase probability density in subensembles of a quantum mode of a one-atom maser

The method of periodic trajectories is applied to the analysis of the phase states of a one-atom maser mode, information on which can be obtained from a series of consequent indirect phase-sensitive quantum measurements of atoms leaving the cavity. Such information allows one to study in detail the evolution of a maser mode in a stationary state. The evolution pattern is represented as a random sequence of subensembles in which the mode exists during different time intervals. An approximate stochastic recurrence relation is obtained, which allows us, using the Monte Carlo method, to generate a sequence of relative frequencies of detection of the states of a chosen basis in escaping atoms. Formulas for the phase probability density for subensembles of the mode are derived. These formulas are obtained using as initial data the average relative frequencies measured by an experimenter in a region of a stable trajectory.     

Generation of a coherent state of the micromaser field

It is found that a coherent state of the cavity field can be generated in a micromaser with injected atoms in a coherent superposition of the upper and lower states. The dependence of the density matrix elements of the field on the number of injected atoms indicates that due to the same initial atomic coherence the emission of separately injected single atoms in the cavity is a cooperative process.Dedicated to Prof. Asim Barut on the occasion of his 65th birthday. Physicist, philosopher, friend of man, here indeed is a role model for us all.     

Quantum phase properties of the field in a two-photon micromaser

In this paper, we study the quantum phase properties of the field in a two-photon micromaser, including the effects of the finite detuning of the intermediate level. For initial coherent state of the cavity field and atoms initially in their excited state multipeak phase structure appears which eventually leads to the randomization of the cavity field phase. However, the approach towards the randomization depends upon the detuning. If the atoms are injected in a coherent superposition of their upper and lower atomic states then the phase distribution evolves into two-peak structure. For initial thermal state and atoms in polarized state, cavity field acquires some phase. We also consider the effect of finite Q of the cavity, random injection of the atoms and fluctuations in the interaction time.     

Role of spatial mode function in the presence of two-atom events in a micromaser

In this paper, we discuss the effects of spatial mode function in an one-photon micromaser in the presence of two-atom events. It is shown that two-atom events allow us a possibility to study the effects of different cavity eigenmodes in a micromaser. We find that squeezing properties of the radiation field depend upon the parity (odd or even) and order (lower or higher) of cavity eigenmodes. For example, squeezing can be obtained for odd-order cavity eigenmodes which completely vanishes for even-order modes. Our results also show that effects similar to self-induced transparency are never obtained in the presence of two-atom events. Finally, we consider the effect of pump fluctuations and cavity losses in our system.     

How to measure the decoherence of a micromaser field under well controlled conditions

We discuss a possible realization of a quantum register with controllable decoherence in terms of /0> and /1> photon number states of a micromaser field. It is shown how to create in the Jaynes-Cummings model a superposition state of /0> and /1> photon number states inside a closed micromaser cavity. The loss of phase coherence between these two states can subsequently be measured by a second probe atom monitoring the decoherence of the field. A technique is proposed for forming the superposition of number states /0> and /1> using the time structure of the Rabi oscillation. The proposed method avoids problems with stray fields at the cavity holes, which disturb the coherence of the atomic superposition, and offers a way to study how the coupling strength to the environment influences the decoherence rate, displaying the robustness of physical qubits and the fidelity of quantum computations.     

Testing a Bell-type inequality with a micromaser

We propose a phase-sensitive micromaser setup to demonstrate experimentally a violation of a Bell-type inequality. The interaction of atoms with the cavity field produces entanglement between the atoms and the cavity photons and therefore also between the atoms. We derive a Bell-type inequality for the atom-atom correlations and show that it can be violated not only in an idealized model but also under realistic circumstances when various sources of additional randomness are accounted for. Among them are the energy dissipation in the resonator and the Poissonian arrival statistics of the atoms.Prof. F.P. Schäfer on the occasion of his 65th birthday.     

Sub-Poisson Distribution of a Radiation Field in a Cascade Three-Level Atomic System

In a cascade three-level atomic system, a parametric study of sub-Poisson or super-Poisson distribution of a stimulated field was performed. By numerical calculation and figures, we investigated the. time evolution of the sub-Poisson distribution of a radiation field. We found that different atomic initial states and different ratios of photon numb& of two radiation fields as well as different ratios of two transitions have a remarkable influence on this distribution. It is interesting to note that under certain conditions, in this cascade structure, there is a high degree of super-Poisson distribution that has not been reported in other structures. We try to explore this anomaly in detail.     

Effect of the spatial inhomogeneity of a field in a micromaser experiment with the selective measurement of atomic states

It is shown that the theoretical analysis of a micromaser experiment with the selective measurement of atomic states is impossible without consideration of the spatial structure of the field and of the statistical spread of the atomic velocities in the cavity. An approximate theory, ignoring the dynamic effects associated with the mentioned factors, yields not only quantitatively, but also qualitatively different theoretical predictions. The dynamics of the field and the mean number of photons in the trapping states realized in this case differ significantly from the predictions of the idealized standard theory used at present. Along with the process of establishment of the stationary Fock state of the field, under certain conditions, it appears possible to form the quasistationary quantum state of the field with large fluctuations of the number of photons, accompanied by the exit of the field from the cavity (“quasi-dissipation”), and the following stepwise transition into the state of the electromagnetic vacuum. It is shown that, under the conditions of the micromaser experiment, the information about the states of atoms, passed through the cavity, in the case considered, does not allow one to draw an unambiguous conclusion about the state of the field in the cavity.     

Dynamics of dispersive photon-number QND measurements in a micromaser

A numerical analysis of dispersive quantum nondemolition measurement of the photon number of a microwave cavity field is presented. Simulations show that a key property of the dispersive atom-field interaction used in Ramsey interferometry is the extremely high sensitivity of the dynamics of atomic and field states to basic parameters of the system. When a monokinetic atomic beam is sent through a microwave cavity, a qualitative change in the field state can be caused by an uncontrollably small deviation of parameters (such as atom path length through the cavity, atom velocity, cavity mode frequency detuning, or atom-field coupling constants). The resulting cavity field can be either in a Fock state or in a super-Poissonian state (characterized by a large photon-number variance). When the atoms have a random velocity spread, the field is squeezed to a Fock state for arbitrary values of the system’s parameters. However, this makes detection of Ramsey fringes impossible, because the probability of detecting an atom in the upper or lower electronic state becomes a random quantity almost uniformly distributed over the interval between zero and unity, irrespective of the cavity photon number.     

Features of the photon statistics of two coupled electromagnetic field modes under the conditions of strong mode coupling

The probabilities of transitions between the Fock states of two electromagnetic field modes under the influence of coupling between modes of finite duration are investigated. It is shown that the transition probability is a strongly oscillating function of the mode numbers of the photons. Under conditions in which the coupling frequency exceeds the geometric mean of the mode frequencies (strong coupling), large numbers of photons are excited in the mode with the lower frequency. The excitation of a two-dimensional radiation field oscillator and the “red” asymmetry of the transition probabilities can be attributed to instability of the classical two-dimensional oscillator with strong mode coupling. Zh. éksp. Teor. Fiz. 112, 128–136 (July 1997)     

Magnetostatic mode in a sheared magnetic field

The effect of magnetic shear on the magnetostatic mode is considered. It is found that the lifetime of the mode is shortened, leading to a reduction of the corresponding cross-field diffusion.     

Generation of pure states in a nondegenerate two-photon micromaser

The generation of two-mode pure states in a lossless nondegenerate two-photon micromaser has been analyzed. The results show that under appropriate conditions, the field may evolve to pure states which can exhibit two-mode squeezing, or evolve to two-mode number states.     

Quantum phase properties of the field in a micromaser: Effect of cooperative atomic interactions, cavity losses and pump fluctuations

In this paper, we study the effect of cooperative atomic interactions, cavity losses, and pump fluctuations on quantum phase properties of the field in a one-photon micromaser. We consider, initial coherent state of the radiation field and atoms initially in the excited and coherent superposition of their atomic states, respectively. We find that quantum phase properties of the field in a micromaser are highly sensitive to two-atom events and cavity losses. Both contribute to the randomization of the well-defined phase structure associated with the initial coherent state. However, the approach towards the randomization is quite different in the two cases. We also find that the fluctuations, associated with the random injection of the atoms, affect the phase structure of the coherent state.     

Stark shift contribution to field statistics in a generalized Jaynes-Cummings model

The nonlinear and multiphoton interaction between a single two-level atom and two modes of radiation is studied in a generalized Jaynes-Cummings model. An intensity-dependent level shift is considered. The time evolution operator is obtained. The detuning has a photon number dependence. Different statistical aspects pertaining to either the atom or the fields are calculated. The dipole moment, the dipole-dipole correlation function, as well as the transient spectrum are obtained.     

Transmission of ultracold atoms through a micromaser: detuning effects

The transmission probability of ultracold atoms through a micromaser is studied in the general case where a detuning between the cavity mode and the atomic transition frequencies is present. We generalize previous results established in the resonant case (zero detuning) for the mesa mode function. In particular, it is shown that the velocity selection of cold atoms passing through the micromaser can be very easily tuned and enhanced using a non-resonant field inside the cavity. Also, the transmission probability exhibits with respect to the detuning very sharp resonances that could define single cavity devices for high accuracy metrology purposes (atomic clocks).Received: 25 March 2003, Published online: 17 February 2004PACS: 42.50.-p Quantum optics - 32.80.-t Photon interactions with atoms - 32.80.Lg Mechanical effects of light on atoms, molecules, and ions     

Quantum statistics of field after double-beam two-photon absorption

Two-photon absorption for a collection of unexcited two-level atoms from two beams of light is considered and the statistical properties of the beams after the interaction are investigated. The dynamical behaviour of the beams is described by assuming the atoms maintained with a nearly fixed population distribution. By applying iteration methods the time development for the paired generating functional of the field is obtained and by means of this generating functional paired modal densities are written. The modal densities are then used for discussing the statistical properties of light after the interaction.