We analyze the dynamics of a set of two-level atoms coupled to the electromagnetic environment within a waveguide. This problem is often tackled by assuming a weak coupling between the atoms and the environment as well as the associated Markov approximation. We show that the accuracy of such an approximation may be more limited than in the single-atom case and may also be strongly determined by the presence of collective effects produced by atom-atom interactions. To this aim, we solve the full problem with exact diagonalization and also the time-dependent density matrix renormalization group method, and we compare the result to that obtained within a weak-coupling master equation and with the Dicke approximation. Finally, we study the dynamics of the entanglement within the system when considering several interatomic distances and atomic frequencies.
We analyze the dynamics of a set of two-level atoms coupled to the electromagnetic environment within a waveguide. This problem is often tackled by assuming a weak coupling between the atoms and the environment as well as the associated Markov approximation. We show that the accuracy of such an approximation may be more limited than in the single-atom case and may also be strongly determined by the presence of collective effects produced by atom-atom interactions. To this aim, we solve the full problem with exact diagonalization and also the time-dependent density matrix renormalization group method, and we compare the result to that obtained within a weak-coupling master equation and with the Dicke approximation. Finally, we study the dynamics of the entanglement within the system when considering several interatomic distances and atomic frequencies.
We examine the dynamics of bipartite quantum entanglement between a two-level atom and the electromagnetic field. We begin with the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong-coupling regime. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem under general couplings. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at late times approximates Markovian dynamics.
We derive the stochastic equations and consider the non-Markovian dynamics of a system of multiple two-level atoms in a common quantum field. We make only the dipole approximation for the atoms and assume weak atom–field interactions. From these assumptions, we use a combination of non-secular open- and closed-system perturbation theory, and we abstain from any additional approximation schemes. These more accurate solutions are necessary to explore several regimes: in particular, near-resonance dynamics and low-temperature behavior. In detuned atomic systems, small variations in the system energy levels engender timescales which, in general, cannot be safely ignored, as would be the case in the rotating-wave approximation (RWA). More problematic are the second-order solutions, which, as has been recently pointed out (Fleming and Cummings 2011 Phys. Rev. E 83 031117), cannot be accurately calculated using any second-order perturbative master equation, such as RWA, Born–Markov, Redfield, etc. The latter problem, which applies to all perturbative open-system master equations, has a profound effect upon calculation of entanglement at low temperatures. We find that even at zero temperature all initial states will undergo finite-time disentanglement (sometimes termed ‘sudden death’), in contrast to the previous work. We also use our solution, without invoking the RWA, to characterize the necessary conditions for Dicke subradiance at finite temperature. We find that the sub-radiant states fall into two categories at finite temperature: one that is temperature independent and one that acquires temperature dependence. With the RWA, there is no temperature dependence in any case.
We analyze the dynamics of one and two two-level atoms interacting with the electromagnetic field in the vicinity of an optical nanofiber without making either the Born or the Markov approximations. We model the dielectric response of the nanofiber with a constant dielectric function and the Drude-Lorentz model, observing deviations from the standard super- and subradiant decays. We discuss the validity of approximating the speed of atom-atom communication to the group velocity of the guided field in the presence of nontrivial environment correlations. Our work presents a deeper understanding of the validity of commonly used approximations in recent waveguide QED platforms.
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this study. We use the concurrence function as a measure of quantum entanglement between the two qubits. Two classes of states are studied in detail: Class A is a one parameter family of states which are the superposition of the highest energy |I〉 ≡ |11〉 and lowest energy |O〉 ≡ |00〉 states, υiz, |A〉≡p|I〉+(1−p)|O〉, with 0 ≤ p ≤ 1; and Class B states |B〉 are linear combinations of the symmetric |+〉=12(|01〉+|10〉) and the antisymmetric |−〉=12(|01〉−|10〉) Bell states.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
We analyze the dynamics of quantum beats in a system of two V-type three-level atoms coupled to a waveguide. We show that quantum beats can be collectively enhanced or suppressed, akin to Dicke super- and subradiance, depending on the interatomic separation and the initial correlations between the atoms. In particular, the interference properties of the collective beats are determined by the distance between the atoms modulo the beat wavelength. We study the collective atomic and field dynamics, illustrating a crossover from a Markovian to a non-Markovian regime as the atomic separation becomes sufficiently large to bring memory effects of the electromagnetic environment into consideration. In such a non-Markovian regime, collective quantum beats can be enhanced beyond the Markovian limit as a result of retardation effects. Our results demonstrate the rich interplay between multilevel and multiatom quantum interference effects arising in a system of distant quantum emitters.