This chapter describes how the nonclassical states are peculiarly sensitive to dissipation when the coupling of the field modes to their larger environment is taken into account. Well before the field energy is significantly dissipated, the coherences responsible for the nonclassical behaviour will decay, at a ‘decoherence rate’ determined by the square of the separation of the constituent components of the nonclassical superpositions in phase-space. The Wigner functions for each Fock state component are given by Laguerre polynomials. These interfere to generate the superposition of interest. Coherences are destroyed at a rate which is proportional to the degree of excitation of the system as the system relaxes to a statistical mixture of relevant ‘pointer bases’. The chapter shows how the dissipative environment ‘deconstructs’ the field into its appropriate constituent parts. The chapter examines the Jaynes-Cummings system governed by the Milburn equation and shows how the intrinsic decoherence modifies the time evolution of the atomic inversion.
This chapter describes how the nonclassical states are peculiarly sensitive to dissipation when the coupling of the field modes to their larger environment is taken into account. Well before the field energy is significantly dissipated, the coherences responsible for the nonclassical behaviour will decay, at a ‘decoherence rate’ determined by the square of the separation of the constituent components of the nonclassical superpositions in phase-space. The Wigner functions for each Fock state component are given by Laguerre polynomials. These interfere to generate the superposition of interest. Coherences are destroyed at a rate which is proportional to the degree of excitation of the system as the system relaxes to a statistical mixture of relevant ‘pointer bases’. The chapter shows how the dissipative environment ‘deconstructs’ the field into its appropriate constituent parts. The chapter examines the Jaynes-Cummings system governed by the Milburn equation and shows how the intrinsic decoherence modifies the time evolution of the atomic inversion.
We show how nonclassical states can be constructed by interference amongst constituents in a superposition of basis states (chosen either from a Fock or coherent state basis). Such superpositions are fragile and highly susceptible to dissipation. We discuss the connection between ensemble averages and the evolution of individual realizations using quantum jump and quantum state diffusion models of conditioned measurements, each realization reflecting a particular measurement record. This allows us to distinguish between decoherence, localization and the deconstruction of superpositions into their components.
Milburn has recently proposed [Phys. Rev. A 44, 5401 (1991)] a variation of the Schr\"odinger equation which models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. In this paper we give an exact solution of this equation and apply it to the Jaynes-Cummings model of atom-field interaction with nontrivial dynamics. We show that the intrinsic decoherence is responsible for deterioration of quantum coherence effects in this model, such as revivals of the atomic inversion. We discuss the applicability of the Milburn equation.
Introduction So far, we have discussed closed systems involving a single quantized mode of the field interacting with atoms, as for example in the Jaynes–Cummings model in Chapter 4. As we saw in this model, the transition dynamics are coherent and reversible: the atom and field mode exchange excitation to and fro without loss of energy. As we add more modes for the atom to interact with, the coherent dynamics become more complicated as the relevant atom–field states come in and out of phase and beat together to determine the total state occupation probabilities. As time goes on, these beats get out of phase, leading to an apparent decay of the initial state occupation probability. But at later times, the beating eigenfrequencies get back in phase in a manner rather reminiscent of the Jaynes–Cummings revival discussed earlier in this book, and this leads to a partial recurrence or revival of the initial state probability. The time scale for this partial revival depends on the number of participating electromagnetic field modes and as these increase to the level appropriate for an open system in free space the recurrence disappears off to the remote future, and the exponential decay law appropriate for decay is recovered as an excellent approximation. We have already discussed the origin of spontaneous emission and the Einstein A coefficient using perturbation theory in Chapter 4.
In this paper, we study the multiphoton Jaynes-Cummings model (JCM) governed by the Milburn equation [G. J. Milburn, Phys. Rev. A 44, 5401 (1991); 47, 2415 (1993)], which models the decoherence of a quantum system as the quantum system evolves through intrinsic mechanisms beyond conventional quantum mechanics. We give an exact solution of this equation for the multiphoton Jaynes-Cummings Hamiltonian and apply it to investigate the influence of the intrinsic decoherence on nonclassical effects (atomic inversion, oscillations of the photon-number distribution, squeezing of the cavity field, and photon antibunching) in the JCM. It is shown that during the time evolution, the intrinsic decoherence in the atom-field interaction suppresses these nonclassical behaviors in the JCM.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz