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arXiv:0902.3406 · Europhysics Letters (EPL)

Two atomic quantum dots interacting via coupling to BECs

Anna Posazhennikova, Wolfgang Belzig

Published Sep 1, 2009• 4 citations
arXivHTMLPDF

Abstract

We consider a system of three weakly coupled Bose-Einstein condensates and two atomic quantum dots embedded in the barriers between the condensates. Each dot is coupled to two neighboring condensates by optical transitions and can be described as a two-state system, or a pseudospin 1/2. Although there is no direct coupling between the dots, an effective interaction between the pseudospins is induced due to their coupling to the condensate reservoirs. We investigate this effective interaction, depending on the strengths of the dot-condensate coupling T and the direct coupling J between the condensates. In particular, we show that an initially ferromagnetic arrangement of the two pseudospins stays intact even for large T / J . However, antiferromagnetically aligned spins undergo peculiar “breathing” modes for weak coupling T / J <1, while for strong coupling the behaviour of the spins becomes uncorrelated.

DOI
10.1209/0295-5075/87/56004

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We consider a system of three weakly coupled Bose-Einstein condensates and two atomic quantum dots embedded in the barriers between the condensates. Each dot is coupled to two neighboring condensates by optical transitions and can be described as a two-state system, or a pseudospin 1/2. Although there is no direct coupling between the dots, an effective interaction between the pseudospins is induced due to their coupling to the condensate reservoirs. We investigate this effective interaction, depending on the strengths of the dot-condensate coupling T and the direct coupling J between the condensates. In particular, we show that an initially ferromagnetic arrangement of the two pseudospins stays intact even for large T / J . However, antiferromagnetically aligned spins undergo peculiar “breathing” modes for weak coupling T / J <1, while for strong coupling the behaviour of the spins becomes uncorrelated.
We consider an atomic quantum dot confined between two weakly coupled Bose-Einstein condensates, where the dot serves as an additional tunneling channel. It is shown that the thus-embedded atomic quantum dot is a pseudospin subject to an external torque, and therefore equivalent to a quantum top. We demonstrate by numerical analysis of the time-dependent coupled evolution equations that this microscopic quantum top is very sensitive to any deviation from linear oscillatory behavior of the condensates. For sufficiently strong dot-condensate coupling, the atomic quantum dot can induce or modify the tunneling between the macroscopic condensates in the two wells.
This thesis investigates the dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensate (BEC) via particle exchange and interactions. This is motivated by the possibility of using such a system as a non-destructive probe of the BEC. A review of the physics of a BEC and relevant impurity models is presented. The collisional blockade regime of the AQD is considered, and the AQD is modelled as a spin-1/2 pseudospin. Having expressed the BEC in terms of number and phase, the semi-classical ground state of the system is determined. The fluctuations in number and phase around this ground state are assumed to be small. Using Fermi's golden rule, the decay rates of the system are calculated. The system dynamics are found to be highly dependent on dimensionality and the coupling between AQD and BEC. Having derived the action for this system, it is found that the small phase fluctuation assumption fails in two dimensions and for certain limits in three dimensions. We attempt to circumvent this difficulty using a canonical transformation. The resulting system is related to a biased spin-boson model. Expressing the pseudospin in terms of Schwinger bosons, the self energy for this system is determined. Green's functions for the system are derived by solving Dyson's equation, and a decay rate is extracted. Determining the spin-spin temporal correlation functions by solving the Bethe-Salpeter equation is found to be intractable due to the Schwinger boson number constraint. The possibility of avoiding this problem using the Holstein-Primakoff representation in a large-S generalisation of the AQD states is explored. We find that the pseudospin precession can be controlled by tuning the coupling parameters and the interactions in the BEC. In particular, we found two unexpected regimes where the pseudospin precession can be slowed down to arbitrarily small frequencies.
We study the dynamics of an atomic quantum dot, i.e., a single atom in a tight optical trap which is coupled to a superfluid reservoir via laser transitions. Quantum interference between the collisional interactions and the laser induced coupling results in a tunable dot-bath coupling, allowing an essentially complete decoupling from the environment. Quantum dots embedded in a 1D Luttinger liquid of cold bosonic atoms realize a spin-boson model with Ohmic coupling, which exhibits a dissipative phase transition and allows us to directly measure atomic Luttinger parameters.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
We investigate the ground-state properties of spin-orbit coupled Bose-Einstein condensates in spin-dependent optical lattices. The competition between the spin-orbit coupling strength and the depth of the optical lattice leads to a rich phase diagram. Without spin-orbit coupling, the spin-dependent optical lattices separate the condensates into alternating spin domains with opposite magnetization directions. With relatively weak spin-orbit coupling, the spin domain wall is dramatically changed from Néel wall to Bloch wall. For sufficiently strong spin-orbit coupling, vortex chains and antivortex chains are excited in the spin-up and spin-down domains respectively, corresponding to the formation of a lattice composed of meron-pairs and antimeron-pairs in the pseudospin representation. We also discuss how to observe these phenomena in real experiments.
We propose and demonstrate a new approach for realizing spin-orbit coupling with ultracold atoms. We use orbital levels in a double-well potential as pseudospin states. Two-photon Raman transitions between left and right wells induce spin-orbit coupling. This scheme does not require near resonant light, features adjustable interactions by shaping the double-well potential, and does not depend on special properties of the atoms. A pseudospinor Bose-Einstein condensate spontaneously acquires an antiferromagnetic pseudospin texture, which breaks the lattice symmetry similar to a supersolid.