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Entanglement in the ground state of interacting qubits driven by a quantum field

B. M. Rodríguez-Lara, Ray‐Kuang Lee

Published Aug 16, 2010• 0 citations
OpenAlex

Abstract

We study the ground state entanglement properties of a finite size ensemble of interacting qubits driven by a quantized field. In the absence of driving, the system reduces to a Lipkin-Meshkov-Glick model that presents maximal entanglement at the first of a series of quantum phase transitions; i.e. a W-state of the qubit ensemble. We present exact and numerical solutions, within and without the rotating wave approximation, in that order, showing that a large finite probability of having the maximal entangled state in the ground state is preserved in the driven system.

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We study the ground state entanglement properties of a finite size ensemble of interacting qubits driven by a quantized field. In the absence of driving, the system reduces to a Lipkin-Meshkov-Glick model that presents maximal entanglement at the first of a series of quantum phase transitions; i.e. a W-state of the qubit ensemble. We present exact and numerical solutions, within and without the rotating wave approximation, in that order, showing that a large finite probability of having the maximal entangled state in the ground state is preserved in the driven system.
We study the ground state of a finite-size ensemble of interacting qubits driven by a quantum field. We find a maximally entangled WWW state in the ensemble part of the system for a certain region of the coupling parameters. The area of this region decreases as the ensemble size increases and, in the classical limit, becomes the line in parameter space that defines the phase transition of the system. In the classical limit, we also study the dynamics of the system and its transition from order to disorder for initial energies close to the ground-state energy. We find that a critical energy providing this transition is related to the minimum of the projection of the total angular momentum of the quantum system in the zzz direction.
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 study quantum state transfer and multipartite entanglement generation in the ensembles of qubits enclosed by a one-dimensional system of coupled optical cavities. Each cavity contains N qubits whose interaction with the quantum field of their respective cavity is governed by the Dicke Lipkin–Meshkov–Glick model. An excitation initially seeded in the ensemble at the end of the one-dimensional chain of coupled cavities transfers to the corresponding ensemble of the last cavity with success that depends on the mode-ensemble coupling χ , ensemble-mode detuning δ , photon hopping rate λ , and size of a given ensemble N . Suitable choices of such parameters enable overcoming the freezing effect induced by the choice of a far-off detuning regime. We identify working points at which three-ensemble W states and two-ensemble maximally entangled states emerge in the multipartite entanglement dynamics. This study provides a basis for manipulation of quantum states in a multipartite coupled cavity arrangement that may be useful in understanding very complex systems in the field of quantum information processing.
Bipartite and global entanglement are analyzed for the ground state of a system of NNN spin-1∕21∕21∕2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter $\ensuremath{\gamma}$, from a separable $(\ensuremath{\gamma}=\ensuremath{\infty})$ to a maximally entangled state $(\ensuremath{\gamma}=0)$. From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point $\ensuremath{\gamma}=0$: While at $\ensuremath{\gamma}=0$ the entanglement grows logarithmically with the system size with no upper bound, it saturates for $\ensuremath{\gamma}\ensuremath{\ne}0$ at a level only depending on $\ensuremath{\gamma}$.
An open fully connected system of qubits at nonzero temperature is driven within a finite time interval along various paths in the space of its control parameters. The driving leads across finite-size precursors of first- and second-order quantum phase transition from factorized to entangled ground-state phases, aiming at the preparation of the complex ground state of the system at the final parameter point with maximal fidelity. During the drive, the system is coupled to a heat bath at a constant temperature, the dynamics being determined in a nonperturbative way by the method of hierarchical equations of motion. It is shown that the presence of the heat bath in combination with specific patterns of avoided crossings affecting the ground and excited states in the parameter region around the quantum phase transition may considerably improve the fidelity of preparation of the target ground state.