Control of a Bose-Einstein condensate by dissipation: Nonlinear Zeno effect

Shchesnovich, V. S.; Konotop, V. V.

doi:10.1103/physreva.81.053611

Cited by 55 publications

(94 citation statements)

References 26 publications

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“…The non-exponential decay is in contrast to the typical evolution found for quantum many body systems coupled to a Markovian environment. In these systems, the decay is often dominated by an exponential dynamics, as e.g., the counterintuitive Zeno effect [13][14][15][16][17], or the relaxation to a desirable state driven by an artificially engi-neered environment [18,19]. Only recently, first signs of an intriguing slowing down of the heating dynamics for interacting bosonic [20][21][22][23] and fermionic [24] gases and an algebraic decay for a specially designed environment which imprints coherence [25] have been predicted.…”

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Emergence of Glasslike Dynamics for Dissipative and Strongly Interacting Bosons

et al. 2013

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We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are due here to strong interactions. This complex two-stage dynamics reveals information on the level structure of the strongly interacting gas.PACS numbers: 05.70. Ln, 03.75.Kk, 37.10.Jk, Unconventional, non-exponential, relaxation dynamics of a perturbed system towards equilibrium has attracted a lot of interest over decades. Already in 1847, Kohlrausch [1] observed a stretched exponential decay in time t, i.e. e −(t/t0) α with α ∈ (0, 1) and t 0 a positive constant, of the discharge of capacitors fabricated from glasses. Since then, such a decay has been observed in many systems such as molecules and polymers [2,3], spin glasses [4,5], nano-sized magnetic particles [6], and certainly amorphous silicon [7,8].A broad variety of theoretical approaches has been developed to explain the mechanism of this unconventional relaxation dynamics [8][9][10][11]. In many of these approaches, e.g. the treatment of the Griffiths phase in disordered spin systems [12], rare configurations have been identified to play a key role. These configurations have an exponentially small probability to occur, and therefore contribute minimally to the short-time dynamics. However, because their relaxation time scale is very long, these rare configurations can dominate the long time evolution. Rare configurations play an important role in the relaxation dynamics of glasses, where they give rise to stretched exponential decays. We will thus refer to this dynamics induced by rare events as 'glass-like' in the following.In this work, we uncover that also in a quantum many body systems, as the Bose-Hubbard model, the dissipative coupling to a Markovian, i.e. memory-less, environment can cause glass-like dynamics. We show that the long time behaviour in these systems can be dominated by rare configurations. These rare configurations are characterized by a large number of atoms occupying a single lattice site. Increasing the number of atoms on the largely occupied site is associated to a long time scale, since the energetic cost of modifying this kind of configurations is very large. Due to this long time scale, these rare configurations dominate the long time dynamics inducing an unconventional dynamics of stretched exponential form as shown, for the case of local number fluctuations κ = n 2 j − n j 2 (wheren j is the number operator of atoms on site j) in Fig. 1. Additionally, the glass-like dynamics is preceded by an algebraic relaxation process due to the int...

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Emergence of Glasslike Dynamics for Dissipative and Strongly Interacting Bosons

et al. 2013

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“…Similarly, a large difference of the onsite potential, real or imaginary, prevents tunneling of the atoms to the respective lattice site. Another interpretation has been discussed in [75,[137][138][139] in terms of the quantum Zeno effect. The particle losses can be viewed as a continuous measurement of the quantum state of the leaky lattice site.…”

Section: The Quantum Zeno Effectmentioning

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The dissipative Bose-Hubbard model

Kordas

Witthaut

Buonsante

et al. 2015

Eur. Phys. J. Spec. Top.

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Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counterintuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.

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“…Projecting on the degenerate subspace, we obtain A simple analysis of Eq. (23) shows that the interaction energy is minimized when all atoms are in either one of the two Bloch modes ϕ ± . Each of the corresponding Bloch waves is a coherent superposition of the alternating discrete vortices and anti-vortices, each occupying just one of the elementary triangles, with the vortex centers being at the dissipative sites, as is easily seen from Eqs.…”

Section: The Honeycomb Optical Lattice With a Periodic Sublat-timentioning

confidence: 99%

“…Then, the state of the system is given by the density matrix ρ satisfying the quantum master equation in the Lindblad form (see, for more details, Ref. [23] and Ref. [24] for a general discussion)…”

Section: The One-dimensional Lattice With a Periodic Sublattice Omentioning

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State engineering for a Bose-Einstein condensate in an optical lattice by means of a periodic sublattice of dissipative sites

Shchesnovich

2012

Phys. Rev. A

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We introduce the notion of dissipative periodic lattice as an optical lattice with periodically distributed dissipative sites and argue that it allows to engineer unconventional Bose-Einstein superfluids with the complex-valued order parameter. We consider two examples, the one-dimensional dissipative optical lattice, where each third site is dissipative, and the dissipative honeycomb optical lattice, where each dissipative lattice site neighbors three non-dissipated sites. The tight-binding approximation is employed, which allows one to obtain analytical results. In the one-dimensional case the condensate is driven to a coherent Bloch-like state with non-zero quasimomentum, which breaks the translational periodicity of the dissipative lattice. In the two-dimensional case the condensate is driven to a zero quasimomentum Bloch-like state, which is a coherent superposition of four-site discrete vortices of alternating vorticity with the vortex centers located at the dissipative sites.

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Control of a Bose-Einstein condensate by dissipation: Nonlinear Zeno effect

Cited by 55 publications

References 26 publications

Emergence of Glasslike Dynamics for Dissipative and Strongly Interacting Bosons

Emergence of Glasslike Dynamics for Dissipative and Strongly Interacting Bosons

The dissipative Bose-Hubbard model

State engineering for a Bose-Einstein condensate in an optical lattice by means of a periodic sublattice of dissipative sites

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