Spectral collapse via two-phonon interactions in trapped ions

Felicetti, Simone; Pedernales, J. S.; Egusquiza, I. L.; Romero, G.; Lamata, Lucas; Braak, Daniel; Solano, E.

doi:10.1103/physreva.92.033817

Cited by 126 publications

(211 citation statements)

References 48 publications

(70 reference statements)

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“…In Ref. [46], Felicetti et al have proposed to implement this model using a chain of ions in a trap illuminated by two lasers, with the motional degree of freedom of the chain playing the role of the bosonic field. The coupling strength g, qubit energy spacing ω q and bosonic frequency ω are then effective and tunable parameters which depend on the frequencies and amplitudes of the two lasers.…”

Section: Mean-field Analysismentioning

confidence: 99%

“…Its spectrum collapses into a continuous band for a specific value of the coupling strength [42][43][44][45]. In the transition from the strong to the USC regime of the twophoton Rabi model, a continuous symmetry breaks down into a four-folded discrete symmetry, identified by a generalized-parity operator [46]. However, so far there are no known results on the ground state of two-photon models in the many-body limit.…”

Section: Introductionmentioning

confidence: 99%

“…The two-photon DM could be implemented using trapped ions [46], which have been used to realize spin systems composed of hundreds of qubits [47]. Similar schemes can be conceived for other atomic or solid state systems.…”

Section: Introductionmentioning

confidence: 99%

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Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

et al. 2017

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The controllability of current quantum technologies allows to implement spin-boson models where two-photon couplings are the dominating terms of light-matter interaction. In this case, when the coupling strength becomes comparable with the characteristic frequencies, a spectral collapse can take place, i.e. the discrete system spectrum can collapse into a continuous band. Here, we analyze the thermodynamic limit of the two-photon Dicke model, which describes the interaction of an ensemble of qubits with a single bosonic mode. We find that there exists a parameter regime where two-photon interactions induce a superradiant phase transition, before the spectral collapse occurs. Furthermore, we extend the mean-field analysis by considering second-order quantum fluctuations terms, in order to analyze the low-energy spectrum and compare the critical behavior with the one-photon case.

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Section: Mean-field Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

et al. 2017

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“…The two-photon QRM has also been studied for a long time both with the RWA [25] and beyond the RWA [26,27,28]. Recently, a realistic implementation of two-photon quantum Rabi models using trapped ions has been proposed [29], which could reach the coupling region corresponding to the interaction-induced spectral collapse. This feature can only be observed in the deep strong coupling regime of the quantum Rabi model [30] and resembles in this respect the well-known superradiant phase transition of the Dicke model [31].…”

Section: Introductionmentioning

confidence: 99%

Two-photon Rabi model: analytic solutions and spectral collapse

Duan

Xie

Braak

et al. 2016

J. Phys. A: Math. Theor.

102

156

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Abstract. The two-photon quantum Rabi model with quadratic coupling is studied using extended squeezed states and we derive G-functions for Bargmann index q = 1/4 and 3/4. The simple singularity structure of the G-function allows to draw conclusions about the distribution of eigenvalues along the real axis. The previously found picture of the spectral collapse at critical coupling g c has to be modified regarding the low lying states, especially the ground state: We obtain a finite gap between ground state and the continuum of excited states at the collapse point. For large qubit splitting, also other low lying states may be separated from the continuum at g c . We have carried out a perturbative analysis allowing for explicit and simple formulae of the eigenstates. Interestingly, a vanishing of the gap between ground state and excited continuum at g c is obtained in each finite order of approximation. This demonstrates cleary the non-pertubative nature of the excitation gap. We corroborate these findings with a variational calculation for the ground state.

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“…The advent of these impressive experimental results prompts a number of theoretical efforts to give analytical solutions for the quantum Rabi and Dicke models [15,16] by applying various techniques [17][18][19][20][21]. On the other hand, the models are expanded to more general cases, including different qubits [22][23][24][25][26], anisotropic couplings [27][28][29], a finite-size ensemble of interacting qubits [30] and two-photon interactions [31], to name only a few.…”

Section: Introductionmentioning

confidence: 99%

Entanglement dynamics of the ultrastrong-coupling three-qubit Dicke model

2016

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We give an analytical description of the dynamics of the three-qubit Dicke model using the adiabatic approximation in the parameter regime where the qubits transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regimes. Qualitative differences arise when comparing to the single-and two-qubit systems -simple analytic formulas show that three revival sequences produce a three-frequency beat note in the time evolution of the population. We find an explicit way to estimate the dynamics for the qubit-field and qubit-qubit entanglement inside the three-qubit system in the ultra strong coupling regime, and the resistance to the sudden death proves the robustness of the GHZ state.

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Spectral collapse via two-phonon interactions in trapped ions

Cited by 126 publications

References 48 publications

Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

Two-photon Rabi model: analytic solutions and spectral collapse

Entanglement dynamics of the ultrastrong-coupling three-qubit Dicke model

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