The hidden symmetry of the asymmetric quantum Rabi model

Mangazeev, Vladimir V.; Batchelor, Murray T.; Bazhanov, Vladimir V.

doi:10.1088/1751-8121/abe426

Cited by 37 publications

(66 citation statements)

References 20 publications

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“…Here it should be mentioned that the word "hidden" is more used for asymmetric QRM with bias where the parity symmetry is generally broken in the model but there are certain points of bias strength that regain some symmetry. [67][68][69] Here our case is reverse in some sense, the parity symmetry is never broken either for the model or in the GS, but there is a symmetry breaking which is little noticed. Let us decompose the parity into two parts, P = P𝜎 Px where P𝜎 = 𝜎 x reverses the spin while Px = (−1) a † a effectively inverses the spatial space x → −x.…”

Section: Hidden Symmetry Breaking At Transition G 𝝀 Cmentioning

confidence: 99%

From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

Ying

2021

Adv Quantum Tech

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The ground state and excitation gap are studied for the anisotropic quantum Rabi model (QRM) which connects the fundamental QRM and the Jaynes-Cummings model (JCM). While conventionally the ground state has a second-order quantum phase transition in the low frequency limit, turning on finite frequencies sheds a novel light on the phase diagram to illuminate a fine structure of first-order transition series. It is found that the conventional quantum phase transition is accompanied with a hidden symmetry breaking, whereas the emerging series transitions are topological transitions without symmetry breaking. The topological structure of the wave function provides a novel universality classification in bridging the QRM and the JCM among the diversity that arises from finite frequencies. The aspect of topological transitions provides a renewed insight for the role of the counter-rotating interaction. Moreover, it is shown that the conventionally established tricritical point is actually a pentacritical or hexacritical point and following this multicritical point emerges a series of quadruple points. Besides the emerging multicriticality and reformed universality, the result demonstrates that a single-qubit system can even exhibit analogs of topological phase transitions which traditionally occur in condensed matter.

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Section: Hidden Symmetry Breaking At Transition G 𝝀 Cmentioning

confidence: 99%

From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

Ying

2021

Adv Quantum Tech

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“…Since, for any qubit state, P 2 ≡< σ > 2 ≤ 1, the strong constraint (45) means that the only separable density matrix (41) of the two spins compatible with the emergence of a qutrit is the product of two homologous eigenstates of any spin component.…”

Section: Representation Of the Density Matrix In The Qutrit Subspacementioning

confidence: 99%

“…A similar route has recently been used to investigate the dynamics of a pair [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ] or a chain [ 32 , 33 ] of coupled spins (also greater than

) subjected to time-independent and time-dependent [ 34 , 35 , 36 ] external magnetic fields. Symmetry arguments have also been exploited to elegantly bring to light intriguing dynamic features of physical systems living in Hilbert spaces of infinite dimensions [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 ]. In Section 4 it is demonstrated that the time evolution of the two dipolarly coupled spins nests a qutrit subdynamics governed by a Hamiltonian model that is explicitly derived.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Belousov

Man’ko

Migliore

et al. 2022

Entropy

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We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.

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“…Among the generations, the asymmetric quantum Rabi model (A-QRM) has attracted much attention recently [42][43][44][45][46]. The A-QRM contains an extra driving term σ x compare to the standard QRM [29].…”

Section: Introductionmentioning

confidence: 99%

“…The interesting thing is that A-QRM seems to recover the symmetry at some certain values of [29,42,50,51]. Many scholars found that the A-QRM has a hidden symmetry [42][43][44][45]. More recently, an analysis of the energy spectrum of the A-QRM from a numerical point of view reveals that the hidden symmetry manifesting the energy level crossover happens for the driving amplitude equaling to an integer times half of the photon frequency ω [46].…”

Section: Introductionmentioning

confidence: 99%

Entanglement resonance in the asymmetric quantum Rabi model

Shi,

Cong,

Eckle

2021

Preprint

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We investigate the entanglement features in the interacting system of a quantized optical field and a statically driven two-level atom, known as the asymmetric quantum Rabi model (A-QRM). Intriguing entanglement resonance valleys with the increase of the photon-atom coupling strength and peaks with the increase of the driving amplitude are found. It is revealed that both of the two kinds of entanglement resonance are caused by the avoided level crossing of the associated eigenenergies. In sharp contrast to the quantum Rabi model, the entanglement of the A-QRM collapses to zero in the strong coupling regime except that the driving amplitude equals to mω/2, with m being an integer and ω being the photon frequency. Our analysis demonstrates that such entanglement reappearance is induced by the hidden symmetry of the A-QRM. Supplying an insightful understanding on the A-QRM, our result is helpful in exploring the hidden symmetry and in preparing photon-atom entanglement in light-matter coupled system.

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The hidden symmetry of the asymmetric quantum Rabi model

Abstract: The asymmetric quantum Rabi model (AQRM) exhibits level crossings in the eigenspectrum for the values ϵ ∈ 1 2 Z o… Show more

Cited by 37 publications

References 20 publications

From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

Entanglement resonance in the asymmetric quantum Rabi model

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