Discrete quantum breathers: What do we know about them?

Fleurov, V.

doi:10.1063/1.1541151

Cited by 59 publications

(54 citation statements)

References 60 publications

(68 reference statements)

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“…In many cases quantum dynamics is important. Quantum breathers consist of superpositions of nearly degenerate many-quanta bound states, with very long times to tunnel from one lattice site to another [4,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Remarkably quantum breathers, though being extended states in a translationally invariant system, are characterized by exponentially localized weight functions, in full analogy to their classical counterparts.…”

Section: Introductionmentioning

confidence: 99%

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

2007

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We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended states in the normal mode space of the noninteracting system. Weight functions of the eigenstates in the space of normal modes are computed by using numerical diagonalization and perturbation theory. We find that staggered states do not compactify in the dilute limit for large chains.

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Section: Introductionmentioning

confidence: 99%

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

2007

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“…For instance, it was suggested that Josephson junctions operating at higher energies may be used for experiments on quantum chaos [8,9,10]. Another phenomenon is the excitation of quantum breathers (QB) [11,12,13], which are nearly degenerate many-quanta bound states in anharmonic lattices. When such states are excited, the outcome is a spacially localized excitation with a very long time to tunnel from one lattice site to another.…”

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confidence: 99%

Quantum localized modes in capacitively coupled Josephson junctions

Pinto

Flach

2007

Europhys. Lett.

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We consider the quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. Quantum breather states are found in the middle of the energy spectrum of the confined nonescaping states of the system. They are characterized by a strong excitation of one junction. These states perform slow tunneling motion from one junction to the other, while keeping their coherent nature. The tunneling time sensitively depends on the initial excitation energy. By using an external bias as a control parameter, the tunneling time can be varied with respect to the escape time and the experimentally limited coherence time. Thus one can control the flow of quantum excitations between the two junctions.PACS numbers: 63.20. Pw, 74.50.+r, 63.20.Ry Josephson junctions are the subject of extensive studies in quantum information experiments because they possess two attractive properties: they are nonlinear devices, and also show macroscopic quantum behavior [1,2,3]. The dynamics of a biased Josephson junction (JJ) is analogous to the dynamics of a particle with a mass proportional to the junction capacitance C J , moving on a tilted washboard potentialwhich is sketched in Fig.1-b. Here ϕ is the phase difference between the macroscopic wave functions in both superconducting electrodes of the junction, I c is the critical current of the junction, and Φ 0 = h/2e the flux quantum. When the energy of the particle is large enough to overcome the barrier ∆U (that depends on the bias current I b ) it escapes and moves down the potential, switching the junction into a resistive state with a nonzero voltage proportional toφ. Quantization of the system leads to discrete energy levels inside the wells in the potential, which are nonequidistant because of the anharmonicity. Note that even if there is not enough energy to classically overcome the barrier, the particle may perform a quantum escape and tunnel outside the well, thus switching the junction into the resistive state [1]. Thus each state inside the well is characterized by a bias and a statedependent inverse lifetime, or escape rate. Progress on manipulation of quantum JJs includes spectroscopic analysis, better isolation schemes, and simultaneous measurement techniques [2,3,4,5,6,7], and paves the way for using them as JJ qubits in arrays for experiments on processing quantum information. Typically the first two or three quantum levels of one junction are used as quantum bits. Since the levels are nonequidistant, they can be separately excited by applying microwave pulses.So far, the studies on JJ qubits focused on low energy excitations involving the first few energy levels of the junctions. Larger energies in the quantum dynamics of JJs give rise to new phenomena that can be observed by using the already developed techniques for quantum information experiments. For instance, it was suggested that Josephson junctions operating at higher energies may be used for experiments on quantum chaos [8,9,10]. Another phenomenon is the excitation of quantum breathers (Q...

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“…At present, because the occurrence of classical breathers is a relatively well understood phenomena, great attention has been paid to characterize their quantum equivalent, for which less detailed results are known [10]. In the quantum regime, the Bloch theorem applies due to the translational invariance of the lattice.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the corresponding eigenstates cannot localize the energy because they must share the symmetry of the translation operator which commutes with the lattice Hamiltonian. Nevertheless, the nonlinearity is responsible for the occurrence of specific states called multi-quanta bound states [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. A bound state corresponds to the trapping of several quanta over only a few neighbouring sites, with a resulting energy which is less than the energy of quanta lying far apart.…”

Section: Introductionmentioning

confidence: 99%

Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice

Falvo

Pouthier

Eilbeck

2006

Physica D: Nonlinear Phenomena

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By using a Generalized Hubbard model for bosons, the energy transfer in a nonlinear quantum lattice is studied, with special emphasis on the interplay between local and nonlocal nonlinearity. For a strong local nonlinearity, it is shown that the creation of v quanta on one site excites a soliton band formed by bound states involving v quanta trapped on the same site. The energy is first localized on the excited site over a significant timescale and then slowly delocalizes along the lattice. As when increasing the nonlocal nonlinearity, a faster dynamics occurs and the energy propagates more rapidly along the lattice. Nevertheless, the larger is the number of quanta, the slower is the dynamics. However, it is shown that when the nonlocal nonlinearity reaches a critical value, the lattice suddenly supports a very fast energy propagation whose dynamics is almost independent on the number of quanta. The energy is transfered by specific bound states formed by the superimposition of states involving v − p quanta trapped on one site and p quanta trapped on the nearest neighbour sites, with p = 0, .., v − 1. These bound states behave as independent quanta and they exhibit a dynamics which is insensitive to the nonlinearity and controlled by the single quantum hopping constant.

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Discrete quantum breathers: What do we know about them?

Cited by 59 publications

References 60 publications

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

Quantum localized modes in capacitively coupled Josephson junctions

Fast energy transfer mediated by multi-quanta bound states in a nonlinear quantum lattice

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