Dynamics of coupled qubits interacting with an off-resonant cavity

Abstract

We study a model for a pair of qubits which interact with a single off-resonant cavity mode and, in addition, exhibit a direct inter-qubit coupling. Possible realizations for such a system include coupled superconducting qubits in a line resonator as well as exciton states or electron spin states of quantum dots in a cavity. The emergent dynamical phenomena are strongly dependent on the relative energy scales of the inter-qubit coupling strength, the coupling strength between qubits and cavity mode, and the cavity mode detuning. We show that the cavity mode dispersion enables a measurement of the state of the coupled-qubit system in the perturbative regime. We discuss the effect of the direct inter-qubit interaction on a cavity-mediated two-qubit gate. Further, we show that for asymmetric coupling of the two qubits to the cavity, the direct inter-qubit coupling can be controlled optically via the ac Stark effect.

Analysis of current and shot noise correlations in a double quantum dot interferometer with interdot spin interactions

“…Finally, we assume the presence of a direct exchange interaction between dots leading to a Heisenberg Hamiltonian for the spins of the two dots in the case of double occupancy characterized by two parameters -the longitudinal coupling (J z ) causing a nonlinear Zeeman shift and a transversal coupling strength (J n ), which flips the spins. The exchange interaction could arise naturally from tunneling of electrons between dots 26 but also could be induced by, for example, coupling to a superconducting microstrip resonator 27 or by two-photon Raman transitions in an optical microcavity 28,29 . The Hamiltonian for the two dot system is given by 29 :…”

“…The exchange interaction could arise naturally from tunneling of electrons between dots 26 but also could be induced by, for example, coupling to a superconducting microstrip resonator 27 or by two-photon Raman transitions in an optical microcavity 28,29 . The Hamiltonian for the two dot system is given by 29 :…”

Adiabatic State Preparation of Interacting Two-Level Systems

“…We show that ARP remains an effective approach in the interacting case, provided the pulse bandwidth is sufficient to span the spectrum of the collective modes generated by the interactions. Although our model is relatively simple, our results are relevant across a wide range of systems, including cavity QED systems [17], quantum dots [16,22], superconducting qubits [23][24][25] and doped impurities in semiconductors [26].The model we consider consists of a set of N interacting two-level systems driven by an external field (in the rotating wave approximation):where σ i are the Pauli matrices for the two-level system i, and σ ± i = (σ x i ± iσ y i )/2. In this form the two states σ z i = ±1 are understood to correspond to the presence or absence of an excitation of the ith two-level system, e.g., of an exciton in a particular state of a particular quantum dot.…”

“…We show that ARP remains an effective approach in the interacting case, provided the pulse bandwidth is sufficient to span the spectrum of the collective modes generated by the interactions. Although our model is relatively simple, our results are relevant across a wide range of systems, including cavity QED systems [17], quantum dots [16,22], superconducting qubits [23][24][25] and doped impurities in semiconductors [26].…”

“…This model could be realized in precisely engineered cavity [17] or circuit QED [23][24][25] systems. Furthermore, a less idealized model of this form can be used to describe many realizations of interacting qubits, such as coupled quantum dots [16,22]. These systems often exhibit disorder in the energies E and interaction strengths J ij , but the robustness of ARP means the general understanding we obtain of the effect of interactions is applicable.…”