Klein Tunneling of a Quasirelativistic Bose-Einstein Condensate in an Optical Lattice

Salger, Tobias; Grossert, Christopher; Kling, Sebastian; Weitz, Martin

doi:10.1103/physrevlett.107.240401

Cited by 77 publications

(96 citation statements)

References 23 publications

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“…They promise to revolutionize computing technologies allowing us to solve otherwise intractable problems with minimal experimental resources [2]. Several physical models have already been proposed for quantum simulations: quantum phase transitions [3], spin models [4][5][6][7][8][9], quantum chemistry [10,11], particle statistics including anyons [12,13], many-body systems with Rydberg atoms [14], quantum relativistic systems [15][16][17][18][19][20][21][22][23], interacting fermion [24] and fermion-boson [25,26] models, Majorana fermions [27,28], the quantum Rabi model in superconducting qubits [29], and relativistic quantum mechanics in circuit QED [30]. It is known that the computational power of a quantum simulator may overcome that of classical computers.…”

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confidence: 99%

Quantum Simulation of Noncausal Kinematic Transformations

Alvarez-Rodriguez

Casanova²,

Lamata³

et al. 2013

Phys. Rev. Lett.

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We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations, in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system. [27,28], the quantum Rabi model in superconducting qubits [29], and relativistic quantum mechanics in circuit QED [30]. It is known that the computational power of a quantum simulator may overcome that of classical computers. However, the set of operations that we can apply in the former is restricted compared with the versatility of the latter. For example, a wide set of unphysical but computable operations, while formally implementable with universal quantum computers, are not accessible to current quantum simulators.A quantum simulation can be seen as a process in which a quantum system is forced to behave according to a given mathematical model, closely reproducing its dynamics. At the same time, the simulator has a dynamics governed by the fundamental laws of nature. In this sense, we wonder whether quantum simulators may encode processes violating their internal operating rules. In Ref.[31], we gave a first example showing how to implement quantum simulations of phenomena beyond quantum physics. Consequently, a natural question arises: is it possible to simulate processes violating special relativity in a quantum device respecting it?In this Letter, we propose a formalism that allows the implementation of Galilean boosts and, in general, coordinate transformations, as spatial or time parity operations, at any evolution time of a quantum simulation. This is significant to increase the versatility of quantum simulators, enabling the change of reference frame in situ during an experiment. The ability of generating these computable operations allows us to obtain correlations between different reference frames. These correlations include, among others, relevant physical quantities as propagators and self-correlation functions, that would otherwise require full state tomography. Moreover, one could also test and analyze the ultimate limits of a quantum simulator, exploring the exciting possibility of implementing noncausal kinematics as, e.g., instantaneous translations or boosts in a controllable quantum platform. This kind of formalism may also give the capability to probe the boundary between physical and unphysical evolution. We will present the proposed method in the context of linear coordinate transformations, where the Galileo group is included. Moreover, this proposal also allows the implementation of nonlinear coordinate transformations, as is the case of...

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confidence: 99%

Quantum Simulation of Noncausal Kinematic Transformations

Alvarez-Rodriguez

Casanova²,

Lamata³

et al. 2013

Phys. Rev. Lett.

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“…A remarkable example is provided by electronic transport in graphene, a carbon mono layer of honeycomb shape, where the energy dispersion relation near a Dirac point resembles the dispersion of relativistic electrons [23]. Experimental evidences for KT have been reported in graphene heterojunctions [6], carbon nanotubes [8], cold ions in Paul traps [19], cold atoms in optical lattices [20], and photonic superlattices [22].…”

Section: Introductionmentioning

confidence: 99%

“…The observation of KT for a relativistic particle is very challenging, because it would require an ultrastrong field, of the order of the critical field for e − e + pair production in vacuum [2,3], which is not currently available. In recent years, there has been an increased interest in simulating KT in diverse and experimentally accessible physical systems (see, for instance, [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] and references therein). A remarkable example is provided by electronic transport in graphene, a carbon mono layer of honeycomb shape, where the energy dispersion relation near a Dirac point resembles the dispersion of relativistic electrons [23].…”

Section: Introductionmentioning

confidence: 99%

Klein tunneling of two correlated bosons

Longhi

Valle

2013

Eur. Phys. J. B

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Abstract. Reflection of two strongly interacting bosons with long-rage interaction hopping on a onedimensional lattice scattered off by a potential step is theoretically investigated in the framework of the extended Hubbard model. The analysis shows that, in the presence of unbalanced on-site and nearestneighbor site interaction, two strongly correlated bosons forming a bound particle state can penetrate a high barrier, despite the single particle can not. Such a phenomenon is analogous to one-dimensional Klein tunneling of a relativistic massive Dirac particle across a potential step.PACS. 03.75.-b Matter waves -71.10.Fd Lattice fermion models (Hubbard model, etc.)

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“…For example, there is the issue relating to the constructive role which decoherence may play for the stabilization of the asymptotic response, similar to what has been observed with stochastic models operating in the classical regime [38]. Another promising research avenue is the implementation of the tunable dispersion relation, stemming from the Floquet spectrum of temporally-modulated optical lattices, for simulations of relativistic physics effects with ultra-cold atoms [39,40]. Finally, the inclusion of interaction between atoms of a dense condensate [41,42] may open a way to the detection of many-body diabatic Floquet states.…”

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Tuning the Mobility of a Driven Bose-Einstein Condensate via Diabatic Floquet Bands

et al. 2013

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We study the response of ultracold atoms to a weak force in the presence of a temporally strongly modulated optical lattice potential. It is experimentally demonstrated that the strong ac-driving allows for a tailoring of the mobility of a dilute atomic Bose-Einstein condensate with the atoms moving ballistically either along or against the direction of the applied force. Our results are in agreement with a theoretical analysis of the Floquet spectrum of a model system, thus revealing the existence of diabatic Floquet bands in the atom's band spectra and highlighting their role in the non-equilibrium transport of the atoms.PACS numbers: 05.40.Fb, 05.45.Jn, 45.50.Jf Experiments with ultra-cold atomic gases in periodically modulated lattice potentials have shown that these systems represent an attractive testing ground to explore non-equilibrium quantum states [1, 2]. Along these lines, the suppression of tunneling in ac-driven optical lattices was experimentally observed, both in the single-particle Common knowledge in non-equilibrium statistical physics [6] indicates that not only the state of a system shifted from equilibrium but also its response to external perturbations can differ substantially from those exhibited by the system at rest. The equilibrium response of one of the simplest quantum models, a particle placed in a stationary periodic potential, when exposed to a weak constant force F is well understood: On a short-timewhere L is the period of the potential, the particle reacts by moving with the velocity determined by the local slope of the ground-band. On larger time scales, t ≥ 2π /F L, the response evolves into the celebrated phenomenon of Bloch oscillations [7,8]. Weak periodic modulations of the potential can change the response. It has been demonstrated that these can propulse the particle over many Brillouin zones, thus rectifying Bloch oscillations into ballistic transport [9]. This observation, along with the results reported in the abovecited works [3][4][5], are well explained by assuming that the temporal modulations do not push the particle outside the ground band. The single-band approach is justified as long as the driving amplitude remains small, so the observed effects can be attributed to a modulation-induced renormalization of the potential [10,11]. Strong driving, however, intermingles eigenstates of the stationary system and sculptures a new spectrum of time-dependent 'dressed states' [12,13], so that the system dynamics no longer fits the perturbative picture [14]. This idea has been exploited in recent experiments with coherent quantum ratchets [16][17][18] and was also used to create new topological states [19].A distinct feature of strongly driven quantum systems is the presence in their Floquet spectra [20,21] of socalled diabatic bands [22,23]. The states belonging to these bands remain near isolated from the rest of system Hilbert space upon parameter variations. In the quasi-classical limit diabatic bands are also called 'regular bands' because of the correspondence b...

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Klein Tunneling of a Quasirelativistic Bose-Einstein Condensate in an Optical Lattice

Cited by 77 publications

References 23 publications

Quantum Simulation of Noncausal Kinematic Transformations

Quantum Simulation of Noncausal Kinematic Transformations

Klein tunneling of two correlated bosons

Tuning the Mobility of a Driven Bose-Einstein Condensate via Diabatic Floquet Bands

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