We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law. Real quantum systems always interact with the environment. This interaction leads to decoherence, the process by which quantum information is degraded and purely quantum properties of a system are lost. Decoherence provides a theoretical basis for the quantum-classical transition ͓1͔, emerging as a possible explanation of the quantum origin of the classical world. It is also a major obstacle for building a quantum computer ͓2͔ since it can produce the loss of the quantum character of the computer. Therefore a complete characterization of the decoherence process and its relation with the physical properties of the system and the environment is needed for both fundamental and practical purposes.The connection between decoherence and environmental quantum phase transitions has been recently investigated ͓3-5͔. A universal Gaussian decay regime in the fidelity of the system was initially identified, and related to a secondorder quantum phase transition in the environment ͓4͔; as a consequence, the decoherence process was postulated as an indicator of a quantum phase transition in the environment. Subsequently, this analysis was refined, and it was found that the universal regime is neither always Gaussian ͓6͔, nor always related to an environmental quantum phase transition ͓5͔.In this paper we analyze the relationship between decoherence and an environmental excited state quantum phase transition ͑ESQPT͒. We show that the fidelity of a single qubit, coupled to a two-level boson environment, becomes singular when the system-environment coupling energy equals the critical energy for the occurrence of a continuous ESQPT in the environment. Therefore our results establish that a critical phenomenon in the environment entails a singular behavior in the decoherence induced in the central system.An ESQPT is a nonanalytic evolution of some excited states of a system as the Hamiltonian control parameter is varied. It is analogous to a standard quantum phase transition ͑QPT͒, but taking place in some excited state of the system, which defines the critical energy E c at which the transition takes place. We can distinguish between different kinds of ESQPTs. As it is stated in ͓7͔, in the thermodynamic limit a crossing of two levels at E = E c determines a first order ES-QPT, while if the number of interacting levels is locally large at E = E c but without real crossings, the ESQPT is continuous. In th...

The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuousexcited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor ͑or the fidelity͒ goes to zero with a finite-size scaling power law.

We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.PACS numbers: 05.30. Rt, 64.70.Tg, 05.45.Mt, 05.70.Fh The emerging field of excited state quantum phase transitions (ESQPTs) describes the nonanalytical behavior of excited states upon changes of parameters in the Hamiltonian [1][2][3]. This is in direct correspondence to quantum phase transitions (QPTs) [4], but takes place at critical energies above the ground state energy [5]. They entail dramatic dynamic consequences, e.g., environments with ESQPTs lead to enhanced decoherence, which could be a major drawback for building a quantum computer [6]. They appear in models of nuclear physics, such as the interacting Boson model [7,8] and the Lipkin-Meshkov-Glick model (LMG) [9]. In molecular physics, singularities of the density of states (DOS) arise in the vibron model [10], which are closely related to the monodromy in molecular bending degrees of freedom [11]. ESQPTs have been predicted to occur in prominent models of quantum optics such as the Dicke and Jaynes-Cummings models [12,13], too.Despite the striking observation of the QPT in the Dicke and the LMG model [14,15], ESQPTs have so far not been found experimentally for systems different to molecular ones, as the energies at which they occur are difficult to reach with standard techniques. Recently, however, the observation of low-energy singularities of the DOS in twisted graphene layers [16], and monodromy in diverse molecules [11], has opened an increasing interest in the experimental investigation of spectral singularities.Quantum critical behavior is usually defined with respect to system energies [4]. Under the effect of a nonadiabatic external control the energy is not conserved and it is not possible to uniquely define a ground state and the corresponding excited states. In this paper we make use of Floquet theory to introduce the concept of critical quasienergy states (CQS), which are a direct generalization of ESQPTs to driven quantum systems. Our model of choice is a paradigmatic model in the quantum chaos community: the kicked top. Quantum kicked systems play a prominent role in the investigation of quantum signatures of chaos and have intriguing relations to condensed matter systems [17]. Examples of these relations are the metal-supermetal [18] and metaltopological-insulator [19] QPTs in the kicked rotator, which can be thought of as a limiting case of the kicked top. Such a limit is established when the top is restricted to evolve along a small equatorial band, which is topologically equivalent to a cylinder [17].We are motivated by a recent experimental realization of the kicked top with driven ultra-cold Cesiuma...