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Journal of Experimental and Theoretical Physics Letters

Nonexponential dynamics and competition between quasi-trapped states in an N-atomic micromaser

George P. Miroshnichenko, Ilya P Vadeiko, Andrei V. Rybin, JUSSI TIMONEN

Published Nov 1, 2000• 0 citations
Publisher

Abstract

Transient processes are examined for the reduced density matrix (RDM) of the quantum mode of a micromaser pumped by clusters of N two-level atoms. The RDM dynamics consists of the fast and slow stages. The hierarchy of time scales is explained by the fact that the spectrum of the operator of RDM evolution contains groups of eigenvalues concentrated near zero and unity. A convenient basis for describing the fast stage is provided by a set of eigenvectors and adjoint vectors of Jordan cells related to the degenerate zero eigenvalue. The dynamics of the adjoint vector as a function of the number of passed clusters is nonexponential. One adjoint vector transforms jumpwise into the neighboring vector upon the passage of the next cluster. The slow stage of dynamics is controlled by the quasi-trapped states (QTSs) of the field. These states are the generalization of the trapped states of the ideal one-atom model and can be represented as linear combinations of the long-lived eigenvectors of the evolution operator with eigenvalues close to unity. An important feature of the QTSs is their stability to fluctuations of the number of atoms in clusters and to the field relaxation rate.

DOI
10.1134/1.1339897

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Transient processes are examined for the reduced density matrix (RDM) of the quantum mode of a micromaser pumped by clusters of N two-level atoms. The RDM dynamics consists of the fast and slow stages. The hierarchy of time scales is explained by the fact that the spectrum of the operator of RDM evolution contains groups of eigenvalues concentrated near zero and unity. A convenient basis for describing the fast stage is provided by a set of eigenvectors and adjoint vectors of Jordan cells related to the degenerate zero eigenvalue. The dynamics of the adjoint vector as a function of the number of passed clusters is nonexponential. One adjoint vector transforms jumpwise into the neighboring vector upon the passage of the next cluster. The slow stage of dynamics is controlled by the quasi-trapped states (QTSs) of the field. These states are the generalization of the trapped states of the ideal one-atom model and can be represented as linear combinations of the long-lived eigenvectors of the evolution operator with eigenvalues close to unity. An important feature of the QTSs is their stability to fluctuations of the number of atoms in clusters and to the field relaxation rate.
We study the dynamics of the reduced density matrix(RDM) of the field in the micromaser. The resonator is pumped by N-atomic clusters of two-level atoms. At each given instant there is only one cluster in the cavity. We find the conditions of the independent evolution of the matrix elements of RDM belonging to a (sub)diagonal of the RDM, i.e. conditions of the diagonal invariance for the case of pumping by N-atomic clusters. We analyze the spectrum of the evolution operator of the RDM and discover the existence of the quasitrapped states of the field mode. These states exist for a wide range of number of atoms in the cluster as well as for a broad range of relaxation rates. We discuss the hierarchy of dynamical processes in the micromaser and find an important property of the field states corresponding to the quasi-equilibrium: these states are close to either Fock states or to a superposition of the Fock states. A possibility to tune the distribution function of photon numbers is discussed.
The model of a micromaser based on unpolarized N-atom clusters described by the Tavis-Cummings Hamiltonian is considered. The properties of the evolution superoperator Γ( t ) that acts on the reduced density matrix of the field are investigated. This superoperator was found to have an integral of motion that leads to a specific type of the matrix element dynamics called diagonal invariance. The same property also holds for the Liouvillian of the interaction between the field and the thermal bath. Within the framework of the considered micromaser model, the anomalous dependence of the average photon number inside the cavity on the quality factor of the cavity and its temperature was discovered. These features of the field evolution were explained by the existence of eigenstates of Γ( t ), which are localized in the Fock basis and have eigenvalues close to unity. These states were called the quasi-trapped states.
Summary form only given. We consider a N-atom micromaser model described by a hamiltonian. Taking into account field relaxation between consecutive N-atom packets we study dynamics and quasi-stationary states of subsystems in the model. Experimentally, such a system may be realized on a high-density atom flux prepared with help of ultrashort time pulses of exciting laser, in order to achieve small packets and avoid large dispersion of entrance times. For initially diagonal density operator of atoms, the system dynamics and particularly of the field reduced density matrix (RDM) have significant simplification, called diagonal invariance. Under such conditions it was found that the field dynamics might be divided into two stages, a rapid stage and a quasi-stationary stage. This behavior is determined by quasi-trapped states, which are a generalization of well known trapped states in the one-atom micromaser. We want to emphasize that our work raises important questions on a possibility to apply formalism of density matrix for description of such experiments.
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.
We present the theory of a micromaser operating on a cascade three-level atomic transition, which is coupled to two cavity modes satisfying the resonance condition. A numerical approach is employed to integrate the master equation describing the microwave field, allowing us to obtain the semiclassical regime in the limit of large mean photon numbers. We show that the transfer rate from the excited atomic state is very close to 100% over a large interval of variation of the interaction time. The atom - field interaction time may be chosen so as to avoid transitions to the intermediate atomic state when in steady-state operation. In this case, the two cavity modes have nearly the same photon statistics, and the fluctuations in the difference of intensities may be reduced by up to 50% below the classical limit. The intensity correlation between the two cavity modes originates from the possibility of controlling the interaction time, rather than from the simultaneous generation of `twin' photons in a two-photon transition.
We study the dynamics of a micromaser where the pumping atoms are strongly driven by a resonant classical field during their transit through the cavity mode. We derive a master equation for this strongly driven micromaser, involving the contributions of the unitary atom-field interactions and the dissipative effects of a thermal bath. We find analytical solutions for the temporal evolution and the steady state of this system by means of phase-space techniques, providing an unusual solvable model of an open quantum system, including pumping and decoherence. We derive closed expressions for all relevant expectation values, describing the statistics of the cavity field and the detected atomic levels. The transient regime shows the buildup of mixtures of mesoscopic fields evolving towards a super-Poissonian steady-state field that, nevertheless, yields atomic correlations that exhibit stronger nonclassical features than the conventional micromaser.