Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

Dente, Axel D.; Bustos-Marún, Raúl A.; Pastawski, Horacio M.

doi:10.1103/physreva.78.062116

Cited by 52 publications

(85 citation statements)

References 73 publications

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“…Continuum threshold influence on non-exponential decay: a brief review While the short time deviations from exponential decay in quantum mechanics can be viewed as resulting simply from the form of the evolution operator (as demonstrated above), it is the existence of a lower or upper bound (threshold) on the energy continuum in open systems that results in non-exponential decay on long time scales [22,23]. Hence it is rather natural that a discrete eigenvalue appearing in the vicinity of the threshold would result in an enhancement of the non-exponential dynamics, including cases in which the exponential decay vanishes completely [6,[28][29][30][31]88]. In particular, it is argued in Ref.…”

Section: Model I: Survival Probability Near the Ep2amentioning

confidence: 99%

“…We can plug this expression into Eq. (11) to finally obtain the effective eigenvalue equation (6) in which H eff (E) here takes the form…”

Section: Exact Effective Hamiltonian and Generalized Eigenvalue Pmentioning

confidence: 99%

“…Applying our expression for the effective Hamiltonian Eq. (12) in the Schrödinger equation (6) we obtain the dispersion equation for the discrete eigenvalues in quadratic form. The two eigenvalue solutions are given by…”

Section: Exact Effective Hamiltonian and Generalized Eigenvalue Pmentioning

confidence: 99%

“…In many such familiar circumstances, we can generally think of these processes as following a simple exponential decay law. We note from the outset that the exponential decay is associated with the resonance in quantum mechanics [1][2][3][4][5][6][7][8][9][10][11][12][13][14], which can be thought of as a generalized eigenstate that resides outside the ordinary Hilbert space [2-4, 8, 12, 15-19].…”

Section: Introductionmentioning

confidence: 99%

“…which consists of a semi-infinite tight-binding chain with a double-impurity (or qubit) coupled at the endpoint of the chain [6]. Again c † j is the creation operator at the jth chain site while the qubit operators d † A , d † B experience the intra-qubit coupling V and the d † B site is again coupled to the endpoint of the chain with strength g. Each of these models can be considered as variations of the Friedrichs model that has been used to describe resonance phenomena in open systems [4,9].…”

Section: Introductionmentioning

confidence: 99%

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Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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It has been reported in the literature that the survival probability P (t) near an exceptional point where two eigenstates coalesce should generally exhibit an evolution P (t) ∼ t 2 e −Γt , in which Γ is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz, et al., Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify the survival probability exhibits the previously reported modified exponential decay on intermediate timescales, but this is replaced with an inverse power law on very long timescales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all timescales and the heuristic approach fails completely. When the EP2A appears very near the threshold we obtain the novel evolution P (t) ∼ 1 − C1 √ t on intermediate timescales, while further away the parabolic decay (Zeno dynamics) on short timescales is enhanced.

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Section: Model I: Survival Probability Near the Ep2amentioning

confidence: 99%

“…We can plug this expression into Eq. (11) to finally obtain the effective eigenvalue equation (6) in which H eff (E) here takes the form…”

Section: Exact Effective Hamiltonian and Generalized Eigenvalue Pmentioning

confidence: 99%

Section: Exact Effective Hamiltonian and Generalized Eigenvalue Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Garmon

Ordóñez

2017

Journal of Mathematical Physics

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Amplification of non‐Markovian decay due to bound state absorption into continuum

Garmon

Petrosky

Simine

et al. 2012

Fortschritte der Physik

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Key words non-Markovian decay, power law decay, bound stateIt is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time 'near zone' and long time 'far zone.' In the near zone the survival probability falls off according to a t −1 power law, and in the far zone it falls off as t −3 . We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t −1 power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t −1 power law dominates precisely at the point of ejection.

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Resonance Trapping and Dynamical Phase Transitions

Rotter

2010

Int J Theor Phys

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In the non-Hermitian quantum physics, resonance trapping occurs due to width bifurcation in the regime of overlapping resonances. It causes dynamical phase transitions in many-level quantum systems. In the present contribution, three different examples, observed experimentally, are considered. In any case, resonance trapping breaks the symmetry characteristic of the system at low level density due to the alignment of a few states with the scattering states of the environment.Keywords Exceptional points · Dynamical phase transitions · PT symmetry breaking · Phase lapses · Spin swapping Most interesting features of non-Hermitian quantum physics occur in the regime of overlapping resonances. Here, the phases of the eigenfunctions of the Hamiltonian are not rigid [1]. It is possible therefore that some eigenstates of the system align with the scattering states of the environment, while the other ones decouple (more or less) from the environment. This phenomenon, called resonance trapping, is known for many years [2]. It is caused by width bifurcation. Due to this mechanism, non-Hermitian quantum physics is able to describe environmentally induced effects.Some years ago, the question has been studied [3] whether or not the resonance trapping phenomenon is related to some type of phase transition. The study is performed by using the toy modelin the one-channel case and with the assumption that (almost) all crossing (exceptional) points accumulate in one point [4]. It has been found that resonance trapping may be understood, in this case, as a second-order phase transition. The calculations are performed I. Rotter ( )

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Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

Cited by 52 publications

References 73 publications

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

Amplification of non‐Markovian decay due to bound state absorption into continuum

Resonance Trapping and Dynamical Phase Transitions

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