A study is made of quasi-stationary states in a matter system which is under internal exchange-interactions among atoms and coupled to an electromagnetic field, by using a variational method and a unitary transformation; therefrom a photon coherent state is derived, The coherent state is characterized by a cooperative dipole orientation excited in the matter by a coherent light. The matter-field interaction energy term depends on the phase difference between the matter system and the field. When the phase difference equals zero, the coupled system is in the ground state. A thermal equilibrium of the matter system in the molecular field approximation is also studied. It is proved that a phase transition of the second kind occurs. This transition may be followed by coherent resonance scattering processes, even when the dipole excited state decays with a nonradiative relaxation time which is much shorter than the radiative life time.
A study is made of quasi-stationary states in a matter system which is under internal exchange-interactions among atoms and coupled to an electromagnetic field, by using a variational method and a unitary transformation; therefrom a photon coherent state is derived, The coherent state is characterized by a cooperative dipole orientation excited in the matter by a coherent light. The matter-field interaction energy term depends on the phase difference between the matter system and the field. When the phase difference equals zero, the coupled system is in the ground state. A thermal equilibrium of the matter system in the molecular field approximation is also studied. It is proved that a phase transition of the second kind occurs. This transition may be followed by coherent resonance scattering processes, even when the dipole excited state decays with a nonradiative relaxation time which is much shorter than the radiative life time.
A non-relativistic quantum theory of matter-photon interaction is formulated, within the framework of the dipole approximation, by employing a canonical transformation to diago nalize the A' term plus the free photon Hamiltonian. The matter-photon interaction is there by expressed rigorously in a renormalized A·p form. Using this form for the Dicke model of two-level atoms interacting with a single-mode radiation field, we examine a possibility of the occurrence of stationary coherent states which could arise for a photon and atomic polarization as the ground state of the system, deducing a condition for such coherent states. The condition, expressed as an inequality which imposes a stable nontrivial Bloch angle of the uniform atomic polarization, is identical with that for the occurrence of a second order phase transition, and indicates that the non-existence of a second order phase transition pointed out by Rza2ewski et al. io; in fact a consequence of the present treatment of the A' term renormalization. However, a fulfillment of the condition is recovered, if exchange type atom-atom interaction is taken into account in the matter system. We also present a method to construct an effective Hamiltonian of atom-atom interaction which is equivalent to the above Dicke model in the thermodynamic limit.
The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.
A pair of nonidentical two-level atoms, separated by a fixed distance R, interact through photon exchange. The system is described by a state vector which is assumed to be a superposition of four "essential states": (1) the first atom is excited, the second one is in the ground state, and no photon is present, (2) the first atom is in its ground state, the second one is excited, and no photon is present, (3) both atoms are in their ground states and a photon is present, and (4) both atoms are excited and a photon is also present. The system is initially in state (1). The probabilities of each atom being excited are calculated for both the minimally-coupled interaction and the multipolar interaction in the electric dipole approximation. For the minimally-coupled interaction Hamiltonian, the second atom has a probability of being instantaneously excited, so the interaction is not retarded. For the multipolar interaction Hamiltonian, the second atom is not excited before the retardation time, which agrees with special relativity. For the minimally-coupled interaction the nonphysical result occurs because the unperturbed Hamiltonian is not the energy operator in the Coulomb gauge. For the multipolar Hamiltonian in the electric dipole approximation the unperturbed Hamiltonian is the energy operator. An active view of unitary transformations in nonrelativistic quantum electrodynamics is used to derive transformation laws for the potentials of the electromagnetic field and the static Coulomb potential. For a specific choice of unitary transformation the transformation laws for the potentials are used in the minimally-coupled second-quantized Hamiltonian to obtain the multipolar Hamiltonian, which is expressed in terms of the quantized electric and magnetic fields.
We consider the description of the quantum dynamics of a two-level system interacting with a single Glauber coherent mode of the radiation field. An exact solution (within the rotating wave and electric dipole approximations) is provided for both the time-independent and time-dependent Green’s functions for the coupled matter–radiation system. The atom (molecular) transition probabilities are shown to be Poisson averages of the corresponding semiclassical problem when the latter is likewise treated in the rotating wave approximation. At low radiation intensities, the quantum and semiclassical results differ, but at high intensities, they become the same when the average photon number n0 in the field satisfies the condition n01/2≫1. A similar behavior is displayed for the expectation value of the electric field of the coherent mode in the presence of the atom. The spectrum of the radiation, resonantly scattered by the atom, is shown to coincide with the results of Mollow.
We introduce a combination of coherent states as variational test functions for the atomic and radiation sectors to describe a system of N a three-level atoms interacting with a one-mode quantised electromagnetic field, with and without the rotating wave approximation, which preserves the symmetry presented by the Hamiltonian. These provide us with the possibility of finding analytical solutions for the ground and first excited states. We study the properties of these solutions for the V -configuration in the double resonance condition, and calculate the expectation values of the number of photons, the atomic populations, the total number of excitations, and their corresponding fluctuations. We also calculate the photon number distribution and the linear entropy of the reduced density matrix to estimate the entanglement between matter and radiation. For the first time, we exhibit analytical expressions for all of these quantities, as well as an analytical description for the phase diagram in parameter space, which distinguishes the normal and collective regions, and which gives us all the quantum phase transitions of the ground state from one region to the other as we vary the interaction parameters (the matter-field coupling constants) of the model, in functional form.
The possibility of a practically total reduction of quantum photon fluctuations in cw laser radiation is discussed. This effect appears as a result of two-photon radiation absorption using a resonance transition in atoms excited from the ground state to the upper level, relaxing to the other states. For this case the possibility of induced two-photon emission is excluded, that is, the source of additional photon number fluctuations in a field mode.1 In this process the Fock states with the photon number n ≥ 2 are continuously reduced from the coherent state of the excited field. For the large time values of interaction the Fock states |n = 0 > and |n = 1> remain in the field. The effect of spin orientations of photons of the excited field on the quantum noise reduction process for the two-photon absorption by atoms on the transitions between the S → S and S → D terms is analyzed. The possibility of transformation of coherent and thermal fields (λ ≃ 6022 Å and λ = 5787 Å) into quasi-Fock states, as a result of its two-photon resonance absorption by Na homogeneous vapor, is considered.