Critical properties of two-level atom systems interacting with a radiation field

Liberti, Giuseppe Di; Zaffino, Rosa Letizia

doi:10.1103/physreva.70.033808

Cited by 22 publications

(33 citation statements)

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“…After the first derivation due to Hepp and Lieb [11], the thermodynamic properties of the DM have been studied by many authors [12,13,14,15,16,17]. In the thermodynamic limit (N → ∞), the system exhibits a secondorder phase transition at the critical point λ c = ∆ω/2, where the ground state changes from a normal to a superradiant phase in which both the field occupation and the spin magnetization acquire macroscopic values.…”

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Scaling of Berry's phase close to the Dicke quantum phase transition

2006

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We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an N qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent.PACS numbers: 03.65. Vf, 42.50.Fx A considerable understanding of the formal description of quantum mechanics has been achieved after Berry's discovery [1] of a geometric feature related to the motion of a quantum system. He showed that the wave function of a quantum system retains a memory of its evolution in its complex phase, which only depends on the "geometry" of the path traversed by the system. Known as the geometric phase, this contribution originates from the very heart of the structure of quantum mechanics. Historically, the first implicit derivation of geometric phase is to be found in the work of H. C. Longuet-Higgins et al.[2] and G. Herzberg and H. C. Longuet-Higgins [3] on the study of the E ⊗ e Jahn-Teller problem in molecular systems. They showed that the Born-Oppenheimer wave function, if required to be real and smoothly varying, undergoes a sign change (a π geometric phase shift) when the nuclear configuration is brought around a crossing point of the energy levels, i.e. a point where the energy levels become degenerate. The widespread interest in geometric phases is unquestionably due to the work of Berry [1] who put the concept of geometric phase in an unexpectedly general scenario, showing that it is a property of the evolution of any quantum mechanical system. It is then not too surprising how this idea has been so broadly studied and applied to a variety of contexts [4,5].An apparently unrelated area in which a connection with Berry Phase (BP) has been recently drawn is the study of Quantum Phase Transitions (QPT) in manybody systems [6,7,8]. It is a well known fact that QPT [9] are accompanied by a qualitative change in the nature of correlations in the ground state of a quantum system, and describing these changes is clearly one of the major interests in condensed matter physics. In particular, critical points are associated with a non-analytical behavior of the system energy density [9] . It is expected that such drastic changes are reflected in the geometry of the Hilbert space. The geometric phase is able to capture singular behaviors of the wave function, and is therefore expected to signal the presence of QPT. The appearance of non-trivial BP in presence of criticality is also heuris-tically motivated by the fact that QPT arise in correspondence of energy level crossings (in the thermodynamical limit) between ground and excited states [9]. As implicitly suggested by the early work of H. C. , level crossings generate...

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confidence: 99%

Scaling of Berry's phase close to the Dicke quantum phase transition

2006

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“…It exhibits a second-order phase transition [5], which has been studied extensively [6,7,8]. The continued interest in the DM arises from its broad application range [9] and from its rich dynamics, displaying many non-classical features [10,11,12,13].…”

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Scaling behavior of the adiabatic Dicke model

2006

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We analyze the quantum phase transition for a set of N -two level systems interacting with a bosonic mode in the adiabatic regime. Through the Born-Oppenheimer approximation, we obtain the finite-size scaling expansion for many physical observables and, in particular, for the entanglement content of the system. PACS numbers: 64.60. Fr, 03.65.Ud, 05.70.Jk, 73.43.Nq Introduction. Many-body systems have become of central interest in the realm of quantum information theory as training grounds to study static, dynamical and sharing properties of quantum correlations. It has been natural, then, to employ the entanglement as a tool to analyze quantum phase transitions, one of the most striking consequences of quantum correlations in many body systems [1,2,3]. In this letter, we study the Dicke superradiant phase transition and obtain the finite size scaling behavior of the quantum correlations at criticality.The Dicke model (DM) describes the interaction of N two-level systems (qubits) with a single bosonic mode [4], and has become a paradigmatic example of collective quantum behavior. It exhibits a second-order phase transition [5], which has been studied extensively [6,7,8]. The continued interest in the DM arises from its broad application range [9] and from its rich dynamics, displaying many non-classical features [10,11,12,13]. The ground state entanglement of the DM has been recently analyzed [14,15,16], and some aspect of its finite size behavior has been obtained numerically. Finally, Vidal and Dusuel,[17], obtained the critical exponents by a modified Holstein-Primakoff approach.The exact treatment of the finite-size corrections to the Dicke transition is quite complicated and the study of some limiting cases can be useful. In this Letter we analyze the case of N qubits coupled to a slow oscillator. We discuss on equal footings both the finite size and the thermodynamic limit of the model, thus allowing to obtain the phase transition as well as its precursors at finite N . Indeed, we obtain the dominant scaling behavior for some entanglement measures and the entire 1/N expansion for all of the relevant physical observables, such as the order parameter. Concerning the quantum correlations, we argue that what is really relevant for the critical behavior is the bi-partite entanglement between the oscillator mode and the set of two level systems.Adiabatic limit. The interaction of N identical qubits with a bosonic mode is described by the Hamiltonian

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“…To focus on our main idea in the work, we only regard the Dicke system as a simplified model. We would like to point out that many authors have recognized this problem, but there still exist many explorations by using this simplified model [13].…”

Section: Model and Hamiltonianmentioning

confidence: 99%

“…This motivates us to study the quantum decoherence of the extra atom near the critical point of the photon-dressed atomic ensemble, which can also reflect the dynamic sensitivity of the photon-dressed atomic ensemble. By tracing over the degree of freedom of the photondressed atomic ensemble in evolution state (13), the reduced density matrix ρ s (t) = Tr a,b {|Ψ (t) Ψ (t)|} of the detected atom is obtained as…”

Section: Quantum Critical Effectmentioning

confidence: 99%

Dynamic sensitivity of photon-dressed atomic ensemble with quantum criticality

Huang

Liao

et al. 2009

Phys. Rev. A

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We study the dynamic sensitivity of an atomic ensemble dressed by a single-mode cavity field (called a photon-dressed atomic ensemble), which is described by the Dicke model near the quantum critical point. It is shown that when an extra atom in a pure initial state passes through the cavity, the photon-dressed atomic ensemble will experience a quantum phase transition, showing an explicit sudden change in its dynamics characterized by the Loschmidt echo of this quantum critical system. With such dynamic sensitivity, the Dicke model can resemble to the cloud chamber for detecting a flying particle by the enhanced trajectory due to the classical phase transition.

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Critical properties of two-level atom systems interacting with a radiation field

Cited by 22 publications

References 22 publications

Scaling of Berry's phase close to the Dicke quantum phase transition

Scaling of Berry's phase close to the Dicke quantum phase transition

Scaling behavior of the adiabatic Dicke model

Dynamic sensitivity of photon-dressed atomic ensemble with quantum criticality

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