Non-adiabatic transitions in a non-symmetric optical lattice

Morales-Molina, Luis; Reyes, Sebastian

doi:10.1088/0953-4075/44/20/205403

Cited by 10 publications

(16 citation statements)

References 29 publications

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“…The above results are consistent with those given in Ref. [24,48]. The band population can be readily obtained as…”

Section: B Systems With Real Adiabatic Parameterssupporting

confidence: 92%

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Landau-Zener-Stückelberg interferometry in PT -symmetric non-Hermitian models

Shen¹,

Wang²,

Li³

et al. 2019

Phys. Rev. A

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We systematically investigate the non-Hermitian generalisations of the Landau-Zener (LZ) transition and the Landau-Zener-Stückelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behaviour analysed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulae for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasised. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time (PT ) reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualised through the beam intensity profile and the transition probabilitiess measured by the centre of mass of the profile. arXiv:1909.05001v2 [quant-ph]

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“…The above results are consistent with those given in Ref. [24,48]. The band population can be readily obtained as…”

Section: B Systems With Real Adiabatic Parameterssupporting

confidence: 92%

“…Such a property was first noticed in Ref. [48] from a numerical calculation. Despite significant differences between the non-Hermitian and Hermitian LZS interferometry, an important common feature remains.…”

Section: A Adiabatic-impulse Theorymentioning

confidence: 55%

Landau-Zener-Stückelberg interferometry in PT -symmetric non-Hermitian models

Shen¹,

Wang²,

Li³

et al. 2019

Phys. Rev. A

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“…To understand how this becomes possible, consider the propagation of monochromatic light waves of wavelength λ along a curved waveguide structure. This could be a single waveguide, coupled ones, or multiple waveguides (Liu et al, 2019;Longhi, 2009;Morales-Molina and Reyes, 2011;Reyes et al, 2012). Let the waveguide structure be planar, in the plane (x, z); see Fig.…”

mentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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H. Comparison of different methods IV. Interferometry A. Superconducting circuits B. Semiconductor quantum dots C. Donors and impurities (atomic qubits) D. Graphene E. Microscopic systems F. Other systems G. Multilevel systems V. Quantum control A. Coherent control of microscopic and mesoscopic structures B. Universal single-and two-qubit control C. Shortcuts to adiabaticity D. Adiabatic quantum computation VI. Related classical coherent phenomena VII. Conclusion 1. With near-adiabatic limit (Landau) 2. With parabolic cylinder functions (Zener) 3. With contour integrals (Majorana) 4. With WKB approximation and phase integral method (Stückelberg) 5. Duration of the LZSM transition B. Description of a periodically driven two-level system 1. Adiabatic-impulse model a. Adiabatic evolution b. Multiple-passage evolution 2. Rotating-wave approximation (RWA) 3. Floquet theory 4. Rate equation and white noise approach a. Transition rate b. Rate equation c. From Bessel to Airy d. Double-passage regime ReferencesAbbreviations and most-often-used symbols Because this review article is quite long, for the readers' convenience, we present the main abbreviations used. This list also includes some of the topics covered.

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“…Note that S 1 = S 2 in the Hermitian case (α = 0), whereas S 1 = 0, S 2 = 0 at the PT symmetry breaking point (α = α c = 1). The coupled equations (19) can be regarded as a generalization, to the non-Hermitian case, of a multi-level LZ problem [35,36]. A particularly interesting case is that of a shallow potential, corresponding to V 0 2 /(2mR 2 ) (i.e.…”

Section: Multilevel Non-hermitian Landau-zener Transitions and Fmentioning

confidence: 99%

Non-Hermitian quantum rings

Longhi

2013

Phys. Rev. A

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We investigate the spectral and dynamical properties of a quantum particle constrained on a ring threaded by a magnetic flux in presence of a complex (non-Hermitian) potential. For a static magnetic flux, the quantum states of the particle on the ring can be mapped into the Bloch states of a complex crystal, and magnetic flux tuning enables to probe the spectral features of the complex crystal, including the appearance of exceptional points. For a time-varying (linearly-ramped) magnetic flux, Zener tunneling among energy states is realized owing to the induced electromotive force. As compared to the Hermitian case, striking effects are observed in the non-Hermitian case, such as a highly asymmetric behavior of particle motion when reversing the direction of the magnetic flux and field-induced delayed transparency.

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Non-adiabatic transitions in a non-symmetric optical lattice

Cited by 10 publications

References 29 publications

Landau-Zener-Stückelberg interferometry in PT -symmetric non-Hermitian models

Landau-Zener-Stückelberg interferometry in PT -symmetric non-Hermitian models

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Non-Hermitian quantum rings

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