Frequency doubling of Bloch oscillations for interacting electrons in a static electric field

Dias, W. S.; Nascimento, E. M.; Lyra, M. L.; Moura, F. A. B. F. de

doi:10.1103/physrevb.76.155124

Cited by 66 publications

(50 citation statements)

References 59 publications

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“…Such two contributions always add with the same sign, for both repulsive (U 0 40) and attractive (U 0 o0) interactions, and generally are of the same order of magnitude. The bound-particle state thus behaves like a single particle hopping on the 1D lattice, but with a driving force which is doubled as compared with that of a single particle 18,19 and with a modified hopping rate k eff . Note that the effect of direct twoatom tunnelling on the BO dynamics, not considered in previous works 19,20,22 , is to increase the amplitude of the breathing motion (owing to the correction of k eff ), whereas the periodicity of the BO is preserved.…”

Section: Resultsmentioning

confidence: 99%

“…When interactions between particles compete with their mobility, novel dynamical behaviour can arise where particles form bound states 13 and co-tunnel through the lattice 14 . While particle interaction has been generally associated to BO damping [15][16][17] , for few strongly interacting particles it was predicted that bound states undergo fractional BO at a frequency twice (or multiple) that of single-particle BO [18][19][20] . The observation of fractional BO is challenging in condensed-matter systems and up to now has not been achieved even in model systems.…”

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confidence: 99%

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Fractional Bloch oscillations in photonic lattices

et al. 2013

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Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose–Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Fractional Bloch oscillations in photonic lattices

et al. 2013

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“…Now, besides the pure (unbound) states covering the range −4J ≤ E ≤ 4J, there is a band of bound-pair states covering the range U ≤ E ≤ √ U 2 + 16J 2 [22,37]. These bound-pair states play a predominant role in the wavepacket dynamics [13,17,22,[37][38][39]. By assuming a transformation to the center-of-mass coordinate f (n 1 , n 2 ) = e ik(n1+n2)a χ(n 1 − n 2 ) it is possible to show (more technical details are found in ref.…”

Section: Resultsmentioning

confidence: 99%

“…Fundamental effects such as the emergence of correlations in twoparticle quantum walks were recently reported for interacting atoms in an optical lattice [13]. The control over the interacting atoms in the regime where the dynamics is dominated by interparticle interactions made it possible to observe the frequency doubling of Bloch oscillations, predicted for electron systems [22] and recently simulated with photons in a waveguide array [23].…”

Section: Introductionmentioning

confidence: 93%

“…A possible physical realization of the present model consists of two bosonic atoms in an optical lattice under a tilting pulse. It has been recently shown experimentaly that two interacting bosons in a tilted optical lattice [13] has similar features of two interacting charged particles under an external uniforme field [22]. Here, the external field consists of a Gaussian-pulse applied parallel to the chain lenght, which can be expressed as…”

Section: Model and Formalismmentioning

confidence: 99%

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Unidirectional quantum walk of two correlated particles: Manipulating bound-pair and unbound wave-packet components

Buarque¹,

Dias²

2017

Physics Letters A

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We study the unidirectional transport of two-particle quantum wavepackets in a regular onedimensional lattice. We show that the bound-pair state component behaves differently from unbound states when subjected to an external pulsed electric field. Thus, strongly entangled particles exhibit a quite distinct dynamics when compared to a single particle system. With respect to centroid motion, our numerical results are corroborated with an analytical expression obtained using a semiclassical approach. The wavefunction profile reveals that the particle-particle interaction induces the splitting of the initial wavepacket into two branches that propagate with specific directions and drift velocities. With a proper external field tunning, the wavepacket components can perform an unidirectional transport on the same or opposite directions. The amplitude of each mode is related to the degree of entanglement betweem particles, which presents a non-monotonic dependence on the interaction strength.

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Revisiting Bloch oscillations in homogeneous and binary chains from an exact quantum mechanical perspective

Lyra

Caetano

2017

Physica Status Solidi (b)

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We present an exact analytic approach to study Bloch oscillations which allows to study cases where the semiclassical arguments are not valid. The method is focused on the velocity operator V. Two representative examples are addressed here: (i) the superposition of AC and DC electric fields in a one‐dimensional chain and (ii) the binary uni‐dimensional chain under the action of a static electric field. For the first case, it is demonstrated that, depending on the frequency of the AC field, an unidirectional movement emerges whose velocity depends on the magnitude of the AC and DC fields, on the phase of the AC field and on the convolution of the initial wavepacket with itself displaced by one lattice spacement. We also show the limit where the semiclassical approach can be used. For the second case, we show that the transition between two mini‐bands plays a significant role in the dynamics of the electronic wavepacket. In this case, the Bloch oscillations are characterized by two main frequencies and combinations of them.

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Frequency doubling of Bloch oscillations for interacting electrons in a static electric field

Cited by 66 publications

References 59 publications

Fractional Bloch oscillations in photonic lattices

Fractional Bloch oscillations in photonic lattices

Unidirectional quantum walk of two correlated particles: Manipulating bound-pair and unbound wave-packet components

Revisiting Bloch oscillations in homogeneous and binary chains from an exact quantum mechanical perspective

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