Interactions and entanglements in BECs

Burnett, K.; Choi, Seok Jin; Dunningham, Jacob; Morgan, S. A.; Rusch, M.

doi:10.1016/s1296-2147(01)01185-4

Cited by 6 publications

(7 citation statements)

References 19 publications

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“…Remarkably, in itinerant boson systems, the condensate fraction n 0 provides bounds on S 2 (n = 1). Much previous work has discussed the relationship between spatial entanglement and n 0 [24][25][26][27][35][36][37][38][39][40][41][42][43][44][45], but here we focus on particle entanglement. First, S 2 is bounded from below by the single copy entanglement S ∞ , and above by 2S ∞ .…”

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confidence: 99%

Particle entanglement in continuum many-body systems via quantum Monte Carlo

et al. 2014

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Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the Rényi entanglement entropies on a particle bipartition, with general applicability to continuum Hamiltonians via path integral Monte Carlo methods. Via direct simulations of interacting bosons in one spatial dimension, we confirm a logarithmic scaling of the single-particle entanglement entropy with the number of particles in the system. The coefficient of this logarithmic scaling increases with interaction strength, saturating to unity in the strongly interacting limit. Additionally, we show that the single-particle entanglement entropy is bounded by the condensate fraction, suggesting a practical route towards its measurement in future experiments.Traditional two-point correlation functions, and their ability to probe broken symmetries, underlie our modern edifice of condensed matter theory. However, they are known to fail as a foundation for a complete classification of all phases of quantum matter, as demonstrated spectacularly in fractional quantum Hall and other topological phases [1,2]. To remedy this insufficiency, one can construct classifications based on information theory, which is by definition a complete description of all correlations, raising the question of which informationbased quantities are relevant for quantum phases of matter [3]. Bipartite entanglement entropy is a leading candidate, with its usefulness and versatility rapidly increasing along with an understanding of its properties in a variety of quantum phases [4]. For example, the ubiquitous "area law" in the spatial entanglement entropy of the ground state [5,6] has led to ways to classify and characterize quantum phases [7][8][9] and phase transitions [10][11][12] in condensed matter systems, along with elucidating the simulability of quantum models on classical computers [13,14]. Previous work has primarily been based upon modal bipartitions, where the entanglement is between two spatial or momentum subregions. However, in systems of itinerant particles [15], one can choose to bipartition into subsets of particles (Fig. 1) [16][17][18][19][20]. This particle entanglement can give insight into not only quantum correlations due to interaction, but also exchange statistics and indistinguishability [21][22][23].

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confidence: 99%

Particle entanglement in continuum many-body systems via quantum Monte Carlo

et al. 2014

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“…For weak output coupling of a trapped atomic gas below the critical temperature T c , it is shown [17] that there are three components that contribute to the output, i.e., coherent coupling of the condensate, stimulated quantum evaporation of thermal excitations, and the simultaneous appearance of an output atom and an internal excitation, indicating the existence of pair entanglements of atoms in the ground state of the gas. The latter is equivalent to the squeezing of the quantum field that describes the atoms.…”

Section: Pair Entanglement In Four-wave Mixingmentioning

confidence: 99%

“…Since the recent spectacular realization of Bose-Einstein condensation in small atomic samples, [1−4] there has been much theoretical interest focused on the physical properties and nature of Bose-Einstein condensed systems such as atom laser, [5] the establishment of the phase of the condensate, [6,7] coherent tunneling, and the collapses and revivals in both the macroscopic wave function and the interference patterns. [8−16] Recently, K. Burnett et al [17] have shown that collisions, i.e., binary correlations between atoms in Bose-Einstein condensed (BEC) gases, can produce the effective interactions between them. They have also discussed entanglement through interactions, in particular via four-wave mixing of matter waves.…”

Section: Introductionmentioning

confidence: 99%

Quantum Effects of Bose–Einstein Condensates

Zhang

Sun

2004

Commun. Theor. Phys.

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In this paper, we study quadrature squeezings of two Bose–Einstein condensates with collision and nonclassical properties of pair entanglement in four wave mixing in Bose–Einstein condensates. With the aid of a numerical method, we find that the two modes (pair entanglement modes) a1 and a2 may exhibit quadrature squeezing, in which they are affected by the initial phase. It is shown that the two pump modes exhibit the same super-Poissonian distribution. The analysis for the mode-mode correlation shows that there always exists a violation of the Cauchy-Schwartz inequality, which means that correlation between the two pump modes is nonclassical.

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“…see Refs. [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]), the class of models where it could actually be measured has been restricted to those without interactions, or consisting of a small number of particles. A general system with continuous degrees of freedom has an infinite Hilbert space, and thus there is no upper bound on the available entanglement [62,63].…”

Section: Introductionmentioning

confidence: 99%

Path-integral Monte Carlo method for Rényi entanglement entropies

et al. 2014

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We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability and interactions. We present proof-of-principle calculations, and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large scale many-body systems of interacting bosons.

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Interactions and entanglements in BECs

Cited by 6 publications

References 19 publications

Particle entanglement in continuum many-body systems via quantum Monte Carlo

Particle entanglement in continuum many-body systems via quantum Monte Carlo

Quantum Effects of Bose–Einstein Condensates

Path-integral Monte Carlo method for Rényi entanglement entropies

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