Phase transitions and Heisenberg limited metrology in an Ising chain interacting with a single-mode cavity field

Abstract.In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally the Jaynes-Cummings model. As the light-matter coupling is increased into the deep strong coupling regime, the ground state turns from vacuum to become a superradiant state characterized by both atomic and photonic excitations. It is pointed out that all four transitions are of the mean-field type, that quantum fluctuations are negligible, and hence these fluctuations cannot be responsible for the corresponding vacuum instability. In this respect, these are not quantum phase transitions. In the case of the Tavis-Cummings and Jaynes-Cummings models, the continuous symmetry of these models implies that quantum fluctuations are not only negligible, but strictly zero. However, all models possess a non-analyticity in the ground state in agreement with a continuous quantum phase transition. As such, it is a matter of taste whether the transitions should be termed quantum or not. In addition, we also consider the modifications of the transitions when photon losses are present. For the Dicke and Rabi models these non-equilibrium steady states remain critical, while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is completely lost, i.e. in realistic settings one cannot expect a true critical behaviour for the two last models.

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“…In the thermodynamic limit the approximation is indeed exact, see Refs. [8,31]. One can show the exactness very intuitively.…”

Section: The Dicke Modelmentioning

confidence: 97%

Some remarks on ‘superradiant’ phase transitions in light-matter systems

Larson

Irish

2017

J. Phys. A: Math. Theor.

101

116

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“…All of this implies that the scaling of the gap with system size at criticality-thus, the complexity class of the adiabatic quantum algorithm-is the same for both passages. We can then exclude that the coupling of the spins with bosons changes the nature of the quantum phase transition, as occurred in [44]. There, a first order transition-which usually implies an exponentially small gap at criticality [40,45]-appeared in an Ising model where spins are coupled to a bosonic mode in the direction perpendicular to the field and to the one of the spin-spin interactions.…”

Section: Ising Model In Transverse Field With Mediated Interactionsmentioning

confidence: 99%

Quantum annealing in spin-boson model: from a perturbative to an ultrastrong mediated coupling

Pino

García-Ripoll

2018

New J. Phys.

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We study a quantum annealer where bosons mediate the Ising-type interactions between qubits. We compare the efficiency of ground state preparation for direct and mediated couplings, for which Ising and spin-boson Hamiltonian are employed respectively. This comparison is done numerically for a small frustrated antiferromagnet, with a careful choice of the optimal adiabatic passage that reveals the features of the boson-mediated interactions. Those features can be explained by taking into account what we called excited solutions: states with the same spin correlations as the ground-state but with a larger bosonic occupancy. For similar frequencies of the bosons and qubits, the performance of quantum annealing depends on how excited solutions interchange population with local spin errors. We report an enhancement of quantum annealing thanks to this interchange under certain circumstances.

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“…In this work we focus on noiseless quantum metrology of N interacting probe systems described by the Ising Hamiltonian where we are interested in determining the precision with which one can estimate either the strength of the transverse magnetic field, B, or the coupling interaction, J, provided the remaining quantity is known. The Hamiltonian of equation (1) is known to exhibit a phase transition [33], which have been discussed previously in the context of quantum metrology and were shown to be resourceful [34][35][36][37]. Moreover, as the Ising Hamiltonian is entanglement generating [38], it has found applications in ion-trap quantum computing architectures [39,40], where either J or B can be controlled at will by modifying either the separation of the ions, or the global magnetic field strength.…”

Section: Introductionmentioning

confidence: 99%

Quantum metrology for the Ising Hamiltonian with transverse magnetic field

2015

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We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. We focus on the unitary evolutions generated by the Ising Hamiltonian that describes the dynamics of a one-dimensional chain of spins with nearest-neighbour interactions and in the presence of a global, transverse, magnetic field. We analytically solve the problem and show that the precision with which one can estimate the magnetic field (interaction strength) given one knows the interaction strength (magnetic field) scales at the Heisenberg limit, and can be achieved by a linear superposition of the vacuum and N free fermion states. In addition, we show that GreenbergerHorne-Zeilinger-type states exhibit Heisenberg scaling in precision throughout the entire regime of parameters. Moreover, we numerically observe that the optimal precision using a product input state scales at the standard quantum limit.

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Phase transitions and Heisenberg limited metrology in an Ising chain interacting with a single-mode cavity field

Cited by 59 publications

References 38 publications

Some remarks on ‘superradiant’ phase transitions in light-matter systems

Some remarks on ‘superradiant’ phase transitions in light-matter systems

Quantum annealing in spin-boson model: from a perturbative to an ultrastrong mediated coupling

Quantum metrology for the Ising Hamiltonian with transverse magnetic field

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