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Conference on Lasers and Electro-Optics

Dynamics and quasi-stationary states of N-atom micromaser

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

Published Aug 29, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iqec.2000.908071

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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 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.
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 studied a multi-atom model of microlaser. As initial conditions we took diagonal density matrix of atoms in the basis of symmetrized collective states. Under diagnonal invariance taking a place for such initial conditions, we considered peculiarities of dynamics of the field reduced density matrix comparing it with the one-atom case. The field possesses subpoissonian distributions in a quasistationare, which are stable with respect to relaxation and number of atoms fluctuations in a packet. When one does not measure the atomic state on output of the cavity, it is possible to observe a macroscopic superposition of few such subpoissonian distributions. Simulating a measuring process of the atomic state, we found that in the quasistationare at any moment the field appears in one of the states and has a subpoissonian statistics of photons.
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.
Matrix continued fraction methods pioneered previously [1–3] are used to solve essentially exactly the dynamics of the one 85Rb atom micromaser. Ranges of cavity Q values, of average atomic input rates R = T p −1 and of atomic interaction times t int are studied with the principal aim of minimizing the cavity field variance v. As expected for T p ≳ 200t int the system does evolve to a steady state with v < 1 and sub-Poissonian photon statistics. But even Q = 5 × 1010 and temperature T = 0·070 K are apparently insufficient conditions for avoiding evolution to a steady state with v < 0 when t int = 1·54/(44 kHz) unless T p is also substantially reduced. Only in this way is actual trapping state dynamics obtained for this value of t int, while no example is found where the system evolves to v = 0 and a single Fock state is produced. The field variance v considered alone is not a good diagnostic for observing such trapping state dynamics and more information will be needed in order to describe adequately the cavity field.