Avoided crossings in driven systems

Holder, B. P.; Reichl, L. E.

doi:10.1103/physreva.72.043408

Cited by 13 publications

(15 citation statements)

References 24 publications

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“…For example, we examined sharp avoided crossings between states localized in chaotic regions and those localized in integrable ones and demonstrated numerically the concomitant complete exchange of their Husimi structures. 34,38,57 We also showed that an avoided crossing between two mixed states tends to be broader than that between a predominately regular state and a predominately chaotic one. Furthermore, we found that the ␣-step size required to resolve an avoided crossing is correlated with the extent to which the participating states are localized in the chaotic and integrable portions of phase space.…”

Section: Discussionmentioning

confidence: 84%

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Quantization of a free particle interacting linearly with a harmonic oscillator

Mainiero

Porter

2007

Chaos

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We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2819060͔ Typical classical Hamiltonians systems are neither fully integrable nor fully chaotic, but instead possess mixed dynamics, with islands of stability situated in a chaotic sea. In this paper, we investigate the quantization of a recently-studied system with mixed dynamics.1 This example consists of a free particle that moves around a ring that is divided into two regions. At the boundaries between these regions, the particle is kicked impulsively by a harmonic oscillator (in a manner that conserves the system's total energy), but the particle and oscillator otherwise evolve freely. Although the system is not generic, its separation into regular and chaotic components also allows more precise investigations (both classically and quantum-mechanically) than is typically possible, making this an ideal example to achieve a better understanding of the quantization of mixed systems. By examining avoided level crossings and Husimi distributions in the quantum system, we investigate the quantum signatures of mixed dynamics, demonstrating that the Husimi structures of nearby states become mixed and delocalized as chaos becomes a more prominent feature in the classical phase space.

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Section: Discussionmentioning

confidence: 84%

“…This provides an example of a smooth exchange of character in a sharp avoided crossing, which has also been observed in other quantum chaotic systems. 38,57 The avoided crossings that we have observed between chaotic and regular states and between two chaotic states have all been sharp ones.…”

Section: -7mentioning

confidence: 93%

Quantization of a free particle interacting linearly with a harmonic oscillator

Mainiero

Porter

2007

Chaos

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“…where the Floquet HamiltonianĤ F is a Hermitian operator in an extended Hilbert space which has time as a periodic coordinate [18,19,20]. Diagonalization ofĤ F in some appropriate basis in this space yields the Floquet eigenstates and eigenvalues.…”

Section: Stirap Transitions In the Quantum Pendulummentioning

confidence: 99%

“…(11) such that ǫ 0 c,qc , the Floquet eigenvalue in that zone corresponding to the physical state |χ c , is equal to ǫ 0 a,qa and the eigenvalue ǫ 0 b,q b is offset from this value by ∆. The degeneracy of these two eigenvalues and the near-degeneracy of the third requires that any perturbation analysis must be performed in the degenerate form [20]. Therefore, we expand the extended Hilbert space state |φ in powers of the small parameter λ |φ = |φ (0) + λ|φ (1) + λ 2 |φ (2) + .…”

Section: Stirap Transitions In the Quantum Pendulummentioning

confidence: 99%

Stimulated-Raman-adiabatic-passage–like transitions in a harmonically modulated optical lattice

Holder

Reichl

2007

Phys. Rev. A

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We introduce a method for the coherent acceleration of atoms trapped in an optical lattice, using the well-known model for stimulated Raman adiabatic passage (STIRAP). Specifically, we show that small harmonic modulations of the optical lattice amplitude, with frequencies tuned to the eigenvalue spacings of three "unperturbed" eigenstates, reveals a threestate STIRAP subsystem. We use this model to realize an experimentally achievable method for transferring trapped atoms from stationary to motional eigenstates.

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“…[18,19]. For the driven square, two kinds of crossings, sharp and broad, were identified by Timberlake and Reichl [18].…”

Section: Diabatic Switching For Floquet Hamiltoniansmentioning

confidence: 99%

Preparation and control of aligned cyclic rotational states

2013

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Molecules in selected rotational states can remain well aligned for extended periods of time in the presence of an appropriate periodic train of nonresonant laser pulses. Here, we show that these states can be prepared by slowly switching the electromagnetic field amplitude during a sequence of laser pulses. For low-temperature ensembles, a high degree of alignment can be achieved by designing pulse trains that take into account the distribution of avoided crossings between quasienergy curves. Additionally, we present calculations that illustrate several effects causing misalignment. A discussion of subtleties concerning systems with unbounded rotational spectra is also included.

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Avoided crossings in driven systems

Cited by 13 publications

References 24 publications

Quantization of a free particle interacting linearly with a harmonic oscillator

Quantization of a free particle interacting linearly with a harmonic oscillator

Stimulated-Raman-adiabatic-passage–like transitions in a harmonically modulated optical lattice

Preparation and control of aligned cyclic rotational states

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