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arXiv:1408.2304 · Physical Review B

Quantum phase transition in a multiconnected superconducting Jaynes-Cummings lattice

Kangjun Seo, Lin Tian

Published May 26, 2015• 24 citations
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Abstract

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.

DOI
10.1103/physrevb.91.195439

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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.
The rapid progress in quantum technology enables the implementation of artificial many-body systems with correlated photons and polaritons. A multiconnected Jaynes-Cummings (MCJC) lattice can be constructed by connecting qubits and cavities alternately. Such models can be realized with superconducting qubits coupled to superconducting microwave resonators or with quantum dots coupled to optical nanocavities. We study the physical properties of a one-dimensional MCJC lattice using the density-matrix renormalization-group method. This model has an intrinsic symmetry between the left and right qubit-cavity couplings. The competition between these couplings may drive the ground state either to a Mott-insulating phase or to a superfluid phase at integer fillings. We calculate the single-particle and density-density correlation functions, the correlation lengths in the Mott-insulating phase, and the Luttinger parameters in the superfluid phase and determine accurately the critical points that separate these two phases.
Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.
The quantum phase transition between Mott insulator and superfluid is studied in the two-dimensional Jaynes-Cummings square lattice in which the counter-rotating coupling (CRC) is included. Both the ground state and the spectra of low-lying excitations are obtained with use of a sophisticated unitary transformation. This CRC is shown not only to induce a long-range interaction between cavities, favoring the long-range superfluid order, but also to break the conservation of local polariton number at each site, leading to the absence of the Mott lobes in the phase diagram, in sharp contrast with the case without the CRC as well as that of the Bose-Hubbard model.
The Properties of the Mott insulator to superfluid phase transition are obtained through the fermionic approximation in the Jaynes-Cummings-Hubbard model on linear, square, SC, FCC, and BCC Bravais lattices. For varying excitation number and atom-cavity frequency detuning. We find that the Mott lobes and the critical hopping are not scalable only for the FCC lattice. At the large excitation number regime, the critical hopping is scalable for all the lattices and it does not depend on the detuning.
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.