Spontaneous nucleation and dynamics of kink defects in zigzag arrays of trapped ions

Ejtemaee, Sara; Haljan, P. C.

doi:10.1103/physreva.87.051401

Cited by 77 publications

(96 citation statements)

References 48 publications

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“…In fact, the KZM is ubiquitous in nature and regards both classical and quantum phase transitions [5,6]. Experimental evidences have been observed in superfluid 4 He [7,8] and 3 He [9,10], in superconducting films [11] and rings [12][13][14][15][16] and in ion chains [17,18]. Bose-Einstein condensation in trapped cold gases has been considered as an ideal platform for the KZM [19][20][21][22][23]; the system is extremely clean and controllable and particularly suitable for the investigation of interesting effects arising from the spatial inhomogeneities induced by the confinement.…”

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confidence: 93%

Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate

et al. 2013

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When a system crosses a second-order phase transition on a finite timescale, spontaneous symmetry breaking can cause the development of domains with independent order parameters, which then grow and approach each other creating boundary defects. This is known as Kibble-Zurek mechanism. Originally introduced in cosmology, it applies both to classical and quantum phase transitions, in a wide variety of physical systems. Here we report on the spontaneous creation of solitons in Bose-Einstein condensates via the Kibble-Zurek mechanism. We measure the power-law dependence of defects number with the quench time, and provide a check of the Kibble-Zurek scaling with the sonic horizon. These results provide a promising test bed for the determination of critical exponents in Bose-Einstein condensates.The Kibble-Zurek mechanism (KZM) describes the spontaneous formation of defects in systems that cross a second-order phase transition at finite rate [1][2][3][4]. The mechanism was first proposed in the context of cosmology to explain how during the expansion of the early Universe the rapid cooling below a critical temperature induced a cosmological phase transition resulting in the formation domain structures. In fact, the KZM is ubiquitous in nature and regards both classical and quantum phase transitions [5,6]. Experimental evidences have been observed in superfluid 4 He [7,8] and 3 He [9,10], in superconducting films [11] and rings [12][13][14][15][16] and in ion chains [17,18]. Bose-Einstein condensation in trapped cold gases has been considered as an ideal platform for the KZM [19][20][21][22][23]; the system is extremely clean and controllable and particularly suitable for the investigation of interesting effects arising from the spatial inhomogeneities induced by the confinement. Quantized vortices produced in a pancake-shaped condensate by a fast quench across the transition temperature have been already observed [24], but their limited statistics prevented the test of the KZM scaling. The KZM has been studied across the quantum superfluid to Mott insulator transition with atomic gases trapped in optical lattices [25]. Here we report on the observation of solitons resulting from phase defects of the order parameter, spontaneously created in an elongated Bose-Einstein condensate (BEC) of sodium atoms. We show that the number of solitons in the final condensate grows according to a power-law as a function of the rate at which the BEC transition is crossed, consistent with the expectations of the KZM, and provide the first check of the KZM scaling with the sonic horizon. We support our observations by comparing the estimated speed of the transition front in the gas to the speed of the sonic causal horizon, showing that solitons are produced in a regime of inhomogeneous Kibble-Zurek mechanism (IKZM) [21]. Our measurements can open the way to the determination of the critical exponents of the BEC transition in trapped gases, for which so far little information is available [26].The KZM predicts the formation of independen...

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confidence: 93%

Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate

et al. 2013

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“…This in itself is a remarkable observation as a priori there is no reason to expect that nonequilibrium properties are fully determined by equilibrium properties only. Recently, three experiments have measured the Kibble-Zurek mechanism in trapped ions [30][31][32] and verified the predicted KibbleZurek scaling. Present and future experiments as well as theoretical works is expected to study the properties of these kinks [26,33].…”

Section: Martin B Plenio and Alex Retzkermentioning

confidence: 99%

Ion Traps as a testbed of classical and quantum statistical mechanics

Plenio¹,

Retzker²

2013

Annalen der Physik

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The development of statistical mechanics over the last century represents a major advance in the Natural Sciences. It is capable of describing a wide range of phenomena including the properties of phase transitions by reducing the complexity of quantum-many-body systems to simple general principles rooted in statistical methods that hold true in macroscopic systems. These principles apply to a broad range of physical theories, encompassing phenomena that are for example governed by classical, relativistic or quantum physics. While many of these predictions have been confirmed experimentally, the exploration, under highly controlled conditions, of the statistical mechanics of mesoscopic systems and the theoretical prediction of their behavior does still represent a challenge for both theory and experiment. A new avenue towards the controlled exploration of the classical and quantum statistical mechanics of mesoscopic systems has opened up

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“…The energy distribution is concentrated around the midpoints of each jump and thus a two energy lump configuration arise. The reason is the existence of a relative minima of V between each two absolute minima when a > 1 5 , recall formulas (11) and (12). Moreover, because V (φ (j+ 1 2 ) ) = 2(1 − a) the value of the potential at these relative minima is close to zero when a is slightly less than one.…”

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confidence: 99%

“…-Entanglement in systems displaying solitonic solutions has been studied for some specific models [1][2][3][4][5]. Recently, solitons in discrete chains presenting bounded internal modes have received increasing attention from both experimental and theoretical point of view [6][7][8][9][10][11][12][13]. Since solitonic solutions of nonlinear models are characterized by being localized and topologically protected, investigation focusing on their use for quantum information tasks are in progress.…”

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confidence: 99%

Solitons and entanglement in the double sine-Gordon model

Izquierdo

Guilarte

Almeida

2014

J. Phys. B: At. Mol. Opt. Phys.

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The bipartite ground state entanglement in a finite linear harmonic chain of particles is numerically investigated. The particles are subjected to an external on-site periodic potential belonging to a family parametrized by the unit interval encompassing the sine-Gordon potential at both ends of the interval. Strong correspondences between the soliton entanglement entropy and the kink energy distribution profile as functions of the sub-chain length are found.Introduction. -Entanglement in systems displaying solitonic solutions has been studied for some specific models [1][2][3][4][5]. Recently, solitons in discrete chains presenting bounded internal modes have received increasing attention from both experimental and theoretical point of view [6][7][8][9][10][11][12][13]. Since solitonic solutions of nonlinear models are characterized by being localized and topologically protected, investigation focusing on their use for quantum information tasks are in progress. As for example, in [14] the authors studied the behavior of entanglement in a chain of particles using the Frenkel-Kontorova model [15][16][17], and they have investigated the possibility to use solitons as the carrier of quantum information. In this model the particles of the 1-D chain interact by means of an elastic force with the nearest neighbors and are subjected to an on-site (substrate) sine-Gordon potential V . The strength of the elastic couplings g between adjacent particles becomes a parameter in the model which rules the width (proportional to √ g) of the unique soliton energy density lump. The influence of the sG soliton on the bipartite entanglement was analyzed by means of the von Neumann entropy, where one of two sub-blocks which conform the chain is always centered at the kink energy density maximum (kink center). The authors study the dependence of the von Neumann entropy on the size of the subblocks for several values of g, i.e., for several values of the soliton width. The result is that the presence of the soliton enhances the entanglement reaching a maximum when the size of the sub-block coincides approximately with the soliton width. The investigation of this issue in interacting multi-soliton solutions is achieved in [18].Solitons and/or kinks are extended states whose energy densities are spatially localized in bounded regions in contrast with vacuum energy densities which are spatially homogeneous. In scalar field theory on the real line the existence of kinks comes from quantization of solitary wave solutions of the classical field equations. These traveling waves have energy densities showing one or several lumps of energy moving together with their center of mass. Thus, the kink center and the centers and widths of these lumps characterize the extended state, see e.g. [19]. We shall address a system in this class determined by the family of double sine-Gordon potential energy densities:

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Spontaneous nucleation and dynamics of kink defects in zigzag arrays of trapped ions

Cited by 77 publications

References 48 publications

Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate

Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate

Ion Traps as a testbed of classical and quantum statistical mechanics

Solitons and entanglement in the double sine-Gordon model

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