Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1004.5041 · Europhysics Letters (EPL)

Circuit QED scheme for the realization of the Lipkin-Meshkov-Glick model

Jonas Larson

Published Jun 1, 2010• 59 citations
arXivHTMLPDF

Abstract

We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating an effective model for the qubits alone. The characteristic long-range order of the Lipkin-Meshkov-Glick model is here mediated by the cavity field. For a closed qubit system, the inherent second order phase transition of the qubits is reflected in the intensity of the output cavity field. In the broken symmetry phase, the many-body ground state is highly entangled. Relaxation of the qubits is analyzed within a mean-field treatment. The second order phase transition is lost, while new bistable regimes occur.

DOI
10.1209/0295-5075/90/54001

Related papers

Dynamical Quantum Phase Transitions in the Dissipative Lipkin-Meshkov-Glick Model with Proposed Realization in Optical Cavity QED

S. Morrison, A. S. Parkins

We present an optical cavity QED configuration that is described by a dissipative version of the Lipkin-Meshkov-Glick model of an infinitely coordinated spin system. This open quantum system exhibits both first- and second-order nonequilibrium quantum phase transitions as a single, effective field parameter is varied. Light emitted from the cavity offers measurable signatures of the critical behavior, including that of the spin-spin entanglement.

arXiv:0708.2753•Physical Review Letters•Jan 31, 2008•166 citations

Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement

S. Morrison, A. S. Parkins

We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model---an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first- and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.

arXiv:0711.2325•Physical Review A•Apr 8, 2008•74 citations

Fully connected network of superconducting qubits in a cavity

Dimitris I. Tsomokos, Sahel Ashhab, Franco Nori

A fully connected qubit network is considered, where every qubit interacts with every other one. When the interactions between the qubits are homogeneous, the system is a special case of the finite Lipkin–Meshkov–Glick (LMG) model. We propose a natural implementation of this model using superconducting qubits in state-of-the-art circuit QED. The ground state, the low-lying energy spectrum and the dynamical evolution are investigated. We find that, under realistic conditions, highly entangled states of Greenberger–Horne–Zeilinger (GHZ) and W types can be generated. We also comment on the influence of disorder on the system and discuss the possibility of simulating complex quantum systems, such as Sherrington–Kirkpatrick (SK) spin glasses, with superconducting qubit networks.

arXiv:0802.1469•New Journal of Physics•Nov 14, 2008•50 citations

Degeneracy beyond the parity-symmetry protection in the Lipkin-Meshkov-Glick model

Jamil Khalouf-Rivera, Miguel Carvajal, Francisco Pérez-Bernal

Degeneracy patterns in quantum mechanics stem from the system symmetries. In particular, the broken-symmetry phase in the well-known Lipkin-Meshkov-Glick (LMG) model is composed of doubly-degenerate states of different parity. In this work, we show that such doublets can exist even if parity is not conserved. For this purpose, our starting point is an anharmonic LMG Hamiltonian with a second-order ground-state quantum phase transition (GSQPT) and a rich spectrum, with two different excited-state quantum phase transitions. The inclusion in the Hamiltonian of a term inducing a first-order GSQPT breaks the parity symmetry but conserving the exponential degeneracy in the energy doublets. We demonstrate that this phenomenon can be traced back to the existence of a $\mathbb{Z}_2$ symmetry (reflection symmetry) in the system's classical limit phase space that leads to an anti-unitary $\mathbb{Z}_2$ symmetry in the quantum system.

quant-pharXiv:2608.21010•Aug 24, 2026•0 citations

Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system

Yuan Zhou, Sheng-li Ma, Bo Li +3 more

We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG) model with nitrogen-vacancy (NV) center ensembles in diamond magnetically coupled to superconducting coplanar waveguide cavities. With the assistance of external microwave driving fields, we show that the interaction of the NV spins can be easily controlled, and several types of the LMG model can be realized by tuning the different parameters. Under the thermal dynamical limit, the distinct nonequilibrium second-order quantum phase transition of the spin ensemble can be achieved at the critical point. Furthermore, we show that the spin squeezed state can be generated by tailoring the LMG Hamiltonian to possess the two-axis countertwisting form in this hybrid quantum system.

arXiv:1712.06234•Physical Review A•Dec 28, 2017•31 citations

Circuit QED and Sudden Phase Switching in a Superconducting Qubit Array

Lin Tian

Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters.

arXiv:1003.2006•Physical Review Letters•Oct 11, 2010•42 citations
We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating an effective model for the qubits alone. The characteristic long-range order of the Lipkin-Meshkov-Glick model is here mediated by the cavity field. For a closed qubit system, the inherent second order phase transition of the qubits is reflected in the intensity of the output cavity field. In the broken symmetry phase, the many-body ground state is highly entangled. Relaxation of the qubits is analyzed within a mean-field treatment. The second order phase transition is lost, while new bistable regimes occur.
We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model---an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first- and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.
A fully connected qubit network is considered, where every qubit interacts with every other one. When the interactions between the qubits are homogeneous, the system is a special case of the finite Lipkin–Meshkov–Glick (LMG) model. We propose a natural implementation of this model using superconducting qubits in state-of-the-art circuit QED. The ground state, the low-lying energy spectrum and the dynamical evolution are investigated. We find that, under realistic conditions, highly entangled states of Greenberger–Horne–Zeilinger (GHZ) and W types can be generated. We also comment on the influence of disorder on the system and discuss the possibility of simulating complex quantum systems, such as Sherrington–Kirkpatrick (SK) spin glasses, with superconducting qubit networks.
Degeneracy patterns in quantum mechanics stem from the system symmetries. In particular, the broken-symmetry phase in the well-known Lipkin-Meshkov-Glick (LMG) model is composed of doubly-degenerate states of different parity. In this work, we show that such doublets can exist even if parity is not conserved. For this purpose, our starting point is an anharmonic LMG Hamiltonian with a second-order ground-state quantum phase transition (GSQPT) and a rich spectrum, with two different excited-state quantum phase transitions. The inclusion in the Hamiltonian of a term inducing a first-order GSQPT breaks the parity symmetry but conserving the exponential degeneracy in the energy doublets. We demonstrate that this phenomenon can be traced back to the existence of a Z2\mathbb{Z}_2Z2​ symmetry (reflection symmetry) in the system's classical limit phase space that leads to an anti-unitary Z2\mathbb{Z}_2Z2​ symmetry in the quantum system.
We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG) model with nitrogen-vacancy (NV) center ensembles in diamond magnetically coupled to superconducting coplanar waveguide cavities. With the assistance of external microwave driving fields, we show that the interaction of the NV spins can be easily controlled, and several types of the LMG model can be realized by tuning the different parameters. Under the thermal dynamical limit, the distinct nonequilibrium second-order quantum phase transition of the spin ensemble can be achieved at the critical point. Furthermore, we show that the spin squeezed state can be generated by tailoring the LMG Hamiltonian to possess the two-axis countertwisting form in this hybrid quantum system.
Superconducting qubits connected in an array can form quantum many-body systems such as the quantum Ising model. By coupling the qubits to a superconducting resonator, the combined system forms a circuit QED system. Here, we study the nonlinear behavior in the many-body state of the qubit array using a semiclassical approach. We show that sudden switchings as well as a bistable regime between the ferromagnetic phase and the paramagnetic phase can be observed in the qubit array. A superconducting circuit to implement this system is presented with realistic parameters.