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arXiv:1410.8458 · Physical Review B

Sitewise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators

Xiu–Hao Deng, Chunjing Jia, Chih-Chun Chien

Published Feb 23, 2015• 12 citations

Abstract

The Bose-Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator-superfluid (MI-SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photonlike. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations, and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.

DOI: 10.1103/physrevb.91.054515

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The Bose-Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator-superfluid (MI-SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photonlike. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations, and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.

We propose a hybrid quantum architecture for engineering a photonic Mott insulator-superfluid phase transition in a two-dimensional (2D) square lattice of a superconducting transmission line resonator (TLR) coupled to a single nitrogen-vacancy (NV) center encircled by a persistent current qubit. The localization-delocalization transition results from the interplay between the on-site repulsion and the nonlocal tunneling. The phase boundary in the case of photon hopping with real-valued and complex-valued amplitudes can be obtained using the mean-field approach. Also, the quantum jump technique is employed to describe the phase diagram when the dissipative effects are considered. The unique feature of our architecture is the good tunability of effective on-site repulsion and photon-hopping rate, and the local statistical property of TLRs which can be analyzed readily using present microwave techniques. Our work opens new perspectives in quantum simulation of condensed-matter and many-body physics using a hybrid spin circuit-QED system. The experimental challenges are realizable using currently available technologies.

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, where

t

is the hopping matrix element. We also show that the superfluid phase is a polar state as in the case for a spin-1 Bose condensate in a harmonic trap. It is found that the MI phase is strongly stabilized against the SF-MI transition when the number of atoms per site is even, due to the formation of singlet pairs. We derive the effective spin Hamiltonian for the MI phase with one atom per site and briefly discuss the spin order in the MI phase.

The connectivity and tunability of superconducting qubits and resonators provide us with an appealing platform to study the many-body physics of microwave excitations. Here we present a multiconnected Jaynes-Cummings lattice model which is symmetric with respect to the nonlocal qubit-resonator couplings. Our calculation shows that this model exhibits a Mott insulator-superfluid-Mott insulator phase transition at commensurate fillings, featured by symmetric quantum critical points. Phase diagrams in the grand canonical ensemble are also derived, which confirm the incompressibility of the Mott insulator phase. Different from a general-purposed quantum computer, it only requires two operations to demonstrate this phase transition: the preparation and the detection of commensurate many-body ground state. We discuss the realization of these operations in a superconducting circuit.

Spectrum tomography for the energy (

E

) of a ring-shaped Bose-Hubbard circuit is illustrated. There is an inter-particle interaction

U

that controls superfluidity (SF) and the transition to the Mott Insulator (MI) regime. The circuit is coupled to an electromagnetic cavity mode of frequency

ω_0

, and the coupling is characterized by a generalized fine-structure-constant

α

that controls the emergence of superconductivity (SC). The

{(U,α,ω_0,E)}

diagram features SF and SC regions, a vast region of fragmented possibly chaotic states, and an MI regime for large

U

. The mesoscopic version of the Meissner effect and the Anderson-Higgs mechanism are discussed.

Ultracold atoms in optical lattices have proven to be a versatile model system in which strong correlation eﬀects in a many-body quantum system can be studied [1]. The tunability and control over almost all underlying system parameters makes them rather unique and allows one to switch between different ground states of the underlying many-body quantum system. One of the most prominent eﬀects in this respect is the quantum phase transition (QPT) from a superﬂuid (SF) to a Mott insulator (MI) that started the ﬁeld of strong-correlation physics with ultracold gases. First theoretically proposed by Fisher et al. [2], the Bose-Hubbard model (BHM) was introduced into the ﬁeld of ultracold atoms by Jaksch et al. [3], eventually being realized in subsequent experiments [4-7]. This article focuses on giving a brief summary of the main results achieved in the SF-MI transition with ultracold bosons in optical lattices. A brief introduction into the setup of optical lattices is followed by a discussion of key results such as the coherence properties, the density proﬁles, transport properties and SF characteristics across the QPT.

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