Shantanu Agarwal

Tavis-Cummings model beyond the rotating wave approximation: Quasidegenerate qubits

The Tavis-Cummings model for more than one qubit interacting with a common oscillator mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the frequencies of the qubits are much smaller than the oscillator frequency and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single qubit system is extended to the multi-qubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intra-manifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-qubit dynamics that are different from the single qubit case, including calculations of qubit-qubit entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.

Dissipation of the Rabi model beyond the Jaynes–Cummings approximation: quasi-degenerate qubit and ultra-strong coupling

Environmental influences on the dynamics of a coupled qubit-oscillator system are studied analytically in a regime where deviations from the exactly solvable Jaynes–Cummings model are important. We investigate the case of a quasi-degenerate qubit within the ultra-strong coupling regime for which the qubit frequency is much smaller than the frequency of the oscillator, and the coupling between the qubit and the oscillator is large, both of which invalidate the usually employed rotating wave approximation. In contrast to the standard quantum optics master equation, we explicitly take the qubit-oscillator coupling into account while microscopically deriving a dressed state master equation. Using the derived master equation, we discuss a spectroscopic technique which can be used to probe the dressed energy-level structure of the qubit-oscillator system.

MAXIMIZING GENUINE MULTIPARTITE ENTANGLEMENT OF N MIXED QUBITS

Beyond the simplest case of bipartite qubits, the composite Hilbert space of multipartite systems is largely unexplored. In order to explore such systems, it is important to derive analytic expressions for parameters which characterize the systems state space. Two such parameters are the degree of genuine multipartite entanglement and the degree of mixedness of the systems state. We explore these two parameters for an N-qubit system whose density matrix has an X form. We derive the class of states that has the maximum amount of genuine multipartite entanglement for a given amount of mixedness. We compare our results with the existing results for the N = 2 case. The critical amount of mixedness above which no N-qubit X-state possesses genuine multipartite entanglement is derived. It is found that as N increases, states with higher mixedness can still be entangled.

X-matrices as a platform for studying multipartite entanglement

We derive an algebraic formula for the genuinely multipartite entanglement of a N-qubit X state. The entanglement dynamics of a N-qubit GHZ-state is a decoherence scenario. We also show that the mixedness of a state limits its entanglement, and the critical mixedness, beyond which no X-state is entangled, increases with the number of qubits.

Dissipative dynamics of the Rabi model in the quasi-degenerate qubit and ultra-strong coupling regime

We study the dissipative dynamics of a coupled qubit-oscillator system. We restrict our analysis to the quasi-degenerate qubit and ultra-strong coupling regime.

Testing separability of mixed states by looking at them

By focusing on the X-matrix part of a two-qubit density matrix we provide a lower bound for the concurrence. We then generalize the result and provide an algebraic separability test for a mixed bipartite state of arbitrary dimension.