Impurity in a Bose-Einstein condensate in a double well

Abstract

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.Comment: 19 pages, 17 figures. The second version contains minor corrections and some better figures (thicker lines

Critical exponents for an impurity in a bosonic Josephson junction: Position measurement as a phase transition

“…However, above W c the eigenstates typically come in even and odd pairs separated by an exponentially small energy difference and numerical diagonalization routines find it very hard to identify the parity of such eigenvectors. Unless one is careful numerical errors lead to eigenvectors with broken symmetry [17], and this directly impacts our results since it is the critical region we are concerned with in our calculations. We have outlined the resolution to this problem in the Appendix of our previous work [25] where we force the eigenstates to have definite parity by diagonalizing the Hamiltonian in the parity basis.…”

“…In the thermodynamic limit where N → ∞, the ground state of the Dicke model undergoes a second order phase transition due to a spontaneous breaking of Z 2 symmetry at the critical coupling strength λ c = √ ωω 0 /2 [32,33]. This phase transition (PT) bears a very close resemblance to the bifurcation that occurs in the impurity model at [17,25] …”

“…Subsequently, we undertook a study comparing the mean-field and many-body properties and described the appearance of a pitchfork bifurcation in the ground state of the mean-field theory above a certain critical value W c of the boson-impurity interaction strength [17]. The mean-field bifurcation arises from the spontaneous localization of the impurity in one of the wells together with a localization of a majority of bosons in the opposite well (assuming repulsive interactions).…”

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“…To overcome the superposition issue, a more recent proposal based on BEC superfluid current states in the ring geometry, analogous to the superconducting flux qubit [17], has been discussed [18]. More recently, the concept of phononic reservoir via the manipulation of the phononic degrees of freedom has pushed quantum information realizations to another level, comprising the dynamics of impurities immersed in BECs [19][20][21][22][23] and reservoir engineering to produce multipartite dark states [24][25][26][27][28][29]. Another important difference in respect to quantum optical system is the possibility to use phononic reservoirs to test nonMarkovian effects in many-body systems [30,31].…”

Entanglement control via reservoir engineering in ultracold atomic gases

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