Cascade Three-level Atom Research Articles

QUANTUM DYNAMICS OF A CASCADE THREE-LEVEL ATOM INTERACTING WITH COHERENT STATE IN THE COUNTER ROTATING WAVE APPROXIMATION

The dynamics of a cascade three-level atom interacting with the single mode coherent state under the Counter-Rotating-Wave approximation (C-RWA) is investigated.The properties of the mean-photon number (N(t)) and the degree of second-order coherence (g2(t)) are analyzed in this model.The little indentation which represents the quantum noise of the system appears in the evolution curves of the mean-photon number and the degree of second-order coherence under the C-RWA.The quantum noise which is caused by the virtual photon field gradually becomes weak when ω increases.The quantum noise increases when increases.The anti-bunching effect of the system under the C-RWA is stronger than the one under the RWA.Besides,the relation of N(t) and g2(t) with the atom-field coupling constant λ is revealed in our results.

ADIABATIC TRANSITION TRANSFER PHENOMENON OF ELECTRONS AND THE QUANTUM STATISTICAL PROPERTIES OF LIGHT FIELD IN A KERR MEDIUM

We first derive the state vector of a cascade three-level atom interacting with pair coherent states in a kerr medium.It is shown by numerical calculations that the Kerr effect results in the adiabatic transition transfer phenomenon of electrons,and the superstructures in the long-time behavior of the quantum statistical properties of light field appear.

Influence of spontaneous emission on trapping states and start-up times of degenerate two-photon micromasers.

We study degenerate two-photon micromasers pumped by cascade three-level atoms, where each atomic energy level has a different linewidth. Our model allows us to recover the ordinary two-photon micromaser situation when these widths vanish. In the limit of large linewidths we obtain a two-photon laser model. We show that trapping states are extremely sensitive to atomic decay, even when the decay time is small in comparison to the transit time through the cavity. Unlike the one-photon micromaser, they are sensitive to the linewidth of the upper, as well as the lower energy level. We have also studied the effects of atomic decay on the starting time of micromasers and on the noise. We found that there is a significant difference between the behavior of two-photon micromasers and lasers as we change the ratio of the widths of the upper and lower levels.

Phase squeezing in a three-level atom micromaser.

I consider a lossless micromaser with cascade three-level atoms in a coherent superposition of its three levels. I find that for some values of the atomic flight time and some probability amplitudes for the intermediate atomic level, the field evolves to a pure state which is the well-known general squeezed state, and the squeeze and displacement parameters are functions of the atomic input parameters. Therefore it is possible to choose atomic parameters which produce squeezing in the phase or in the amplitude of the field inside the cavity.

Local field effect in the three-level atom

The density matrix evolution for a three-level cascade atom is generalised to high vapour densities by the inclusion of the local field effect, and thereby, nonlinear cross-coupling terms arise. Numerical results show that these do not affect electromagnetically induced transparency significantly at moderate densities. Opportunities for experimental observation of the correction in this, and a resonantly-enhanced sum frequency mixing system, at very high densities, are indicated.

JAYNES-CUMMINGS MODEL OF TWO CASCADE THREE-LEVEL ATOMS AND ITS NONLINEAR PROPERTY

In this paper, we have studied the nonlinear interaction of two cascade three-level atoms with single mode field. The results show that the cooperative emission of two atoms can translate into synchronous when the strength of exciting field reaches a certain threshold, That is self-organization may occur in many-atom system to form a "large atom system" at the thre-shold, producing synchronous ordered emission Meanwhile, the second-order correlation degree of two-atom system is larger than that of single atom system due to the synchronous emission effect, i.e. bunching is strong but antibunching is weak. Moreover, the deeper squeezing of two-atom system is obtained since many-photon processes become stronger, and the stren-gth of exciting field is reguired to be also stronger.

Spectrum of squeezing for two-photon correlated-spontaneousemission lasers

We study the spectrum of squeezing for the two-photon correlated-spontaneousemission lasers (CEL's), which consists of coherently pumped, cascade three-level atoms interacting with a single mode of the cavity field. For the resonant two-photon CEL, the spectrum of squeezing is always lorentzian, and more than 80% extra-cavity squeezing has been found in both the phase-and the amplitude-squeezing cases. For the off-resonant two-photon CEL, we use both the exact interaction hamiltonian and an effective two-photon interaction hamiltonian. While the effective hamiltonian always predicts lorentzian spectrum of squeezing in the phase quadrature, the exact hamiltonian gives non-lorentzian one in general, expecially near threshold. Both hamiltonians predict that maximal (over 90%) extracavity phase squeezing is obtained near threshold with large one-photon detunings and equal initial atomic populations between the upper and lower levels. We also find that the effective hamiltonian underestimates the phase variance outside the cavity.

A STUDY ON DISSIPATION MECHANISM IN TWO-PHOTON LASER

In this work, we have respectively investigated two-photon processes of a cascade three-level atom interacting with thermal and vacuum radiation fields by means of non-relativestic QED. We verified the important role of atomic thermal loss and two-photon transtion loss in the disspation processes. We proved the condition under which the thermal fluctuation can be neglected, and discussed, the character of laser cavity in which the two-photon laser can be produced.

Q-function approach to a two-photon laser.

A quantum theory of a two-photon laser is developed by making use of the antinormal-ordering Q function. Starting from the microscopic atom-field interaction Hamiltonian for cascade three-level atoms and including saturable absorbers, we first present a master equation for the field-density operator, and then transform the master equation into a Fokker-Planck equation for the Q function. The Q-function approach enables us to study the two-photon laser analytically, obtaining simple expressions for nonlinear gain, mean photon number, frequency pulling, natural linewidth, and photon-number variance in a unified method. We find that the field in a two-photon laser will build up from a vacuum without triggering if its linear gain is larger than the cavity loss. Also hysteresis can occur in the two-photon laser even without triggering. With an overall two-photon resonance, the normalized photon-number variance approaches a common value 11/8 well above ``threshold,'' independent of the one-photon detuning. We compare these results with previous results obtained from an effective interaction Hamiltonian. We find that the domain of validity of the effective Hamiltonian for the photon-number variance is much smaller than that for the mean photon number. Well above ``threshold'' the effective Hamiltonian overestimates both the natural linewidth and the photon-number variance.

The antibunching and the quantum beat of the interaction of a cascade three-level atom with two radiation fields

The time evolution of the antibunching and quantum beat is studied by considering the resonant interaction of two radiation fields with a cascade three-level atom. It is found that different initial atomic states and different ratios of the average photon number of two radiation fields as well as the different coupling coefficients have a remarkable influence on the antibunching and quantum beat of two radiation fields. By numerical summation and a number of figures, it is interesting to note that under certain conditions, some strange behaviour occurs in this cascade three-level atomic system. The explanation of these strange behaviours is given.

Quantum theory of two-photon correlated-spontaneous-emission lasers: Exact atom-field interaction Hamiltonian approach.

A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL's) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering Q function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL's analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state Q functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.

Non-classical Features in the Three-level Jaynes-Cummings Model

Abstract The eigenfunctions and eigenenergies of the system composed of a cascade three-level atom and bichromatic or monochromatic field with arbitrary detunings are presented. The development of the state vector of the system with arbitrary initial conditions is obtained. The development of the quantum fluctuations and the second-order coherence degree for the field is calculated. The dependence of the squeezing and antibunching on the detunings, initial intensities and initial squeezing is studied. The contribution of single-photon and two-photon transitions to, and the influence of, the a.c. Stark effect on the squeezing are discussed.

Simultaneous jumps in two two-level atoms

We demonstrate the importance of collective behaviour in two identical two-level atoms. When the atoms become very close together a cascade three-level atom analysis can be adopted to show the increasing possibility of simultaneous jumps. Due to the dipole-dipole interaction the intermediate one-atom excited state is detuned by a large amount when the atoms are close together but leaving the upper two-atom excited state in two-photon resonance. The relative importance of multiple jumps compared with stepwise independent jumps is then changed dramatically.

Squeezing in a three-level Jaynes-Cummings model

The evolution of the state vector of a system composed of a cascade three-level atom and a single-mode field with arbitrary detuning and initial condition has been obtained. The quantum fluctuations of the field are presented. The contribution of single- and two-photon transitions to the squeezing of the field is discussed. The dependence of the squeezing on initial intensities of the field and detuning are given.

SQUEEZING PHENOMENON IN THE CASCADE TWO-PHOTON PROCESS

The Schrodinger's equation method is used to investigate the squeezing phenomenon of the electromagnetic field in the case of a three-level cascade atom interacting with single-mode cavity field. The effects of the stimulating strength and the coupling constants on the squeezing phenomenon are discussed. Furthermore, the roles played by the saturation effect and the two-photon process, and the relation between the 1st order coherence and the squeezing effects of the field are revealed.

ANTIBUNCHING OF THE STIMULATED EMISSION FROM A THREE LEVEL CASCADE ATOM

The second-order correlation functions of the stimulated emisson in the case of a three-level cascade atom interacting with radiation fields initially in coherent states or chaotic states are disccused. It is found that there exists photon antibunching.

A QUANTUM-STATISTICAL THREE-LEVEL CASCADE JAYNES-CUMMINGS MODEL

A quantum-statistical model for a three-level cascade atom interacting with radiation fields initially in coherent states is presented. By means of numerical summation and saddle-point approximation, the expectation values of the atomic-level operators and the photon numbers are obtained and discussed, which reveals the phenomena such -as the twophoton transitions and the new collapse and revival.