Atomic Quantum Dots Coupled to a Reservoir of a Superfluid Bose-Einstein Condensate A. Recati, 1,2 P. O. Fedichev, 1 W. Zwerger, 1 J. von Delft, 3 and P. Zoller 1 1 Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria 2 CRS BEC-INFM, Povo and ECT*, Villazzano, I-38050 Trento, Italy 3 Sektion Physik, Universita ¨t Mu ¨nchen, Theresienstrass 37/III, D-80333 Mu ¨nchen, Germany (Received 4 August 2003; published 2 February 2005) 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. DOI: 10.1103/PhysRevLett.94.040404 PACS numbers: 03.75.Nt, 03.67.–a, 42.50.–p A focused laser beam superimposed to a trap holding an atomic Bose-Einstein condensate (BEC) [1] allows the formation of an atomic quantum dot (AQD), i.e., a single atom in a tight trap [2,3] which is coupled to a reservoir of Bose-condensed atoms via laser transitions. This configu- ration can be created, e.g., by spin-dependent optical po- tentials [4], where atoms in the dot and the reservoir correspond to different internal atomic states connected by Raman transitions. Atoms loaded in the AQD repel each other due to collisional interactions. In the limit of strong repulsion, a collisional blockade regime can be realized where either one or no atom occupies the dot, while higher occupations are excluded. Below we study the dynamics of such an AQD coupled to a BEC reservoir: as the key feature we identify the competition between two types of interactions, namely, the coupling of the atom in the dot to the BEC density fluctuations via collisions, and the laser induced coupling to the fluctuating condensate phase. Depending on the choice of interaction parameters, they can interfere destructively or constructively, providing a tunable coupling of the dot to the phonons in the con- densate in the form of a spin-boson model [5]. In particular, an essentially complete decoupling of the dot from the dissipative environment can be achieved, realizing a per- fectly coherent two-level system. This interference and tunability of the coupling of the dot to the environment occurs for condensates in any dimensions. A particularly interesting case is provided by a 1D superfluid reservoir [6], i.e., a bosonic Luttinger liquid of cold atoms [7], where the system maps to a spin-boson model with Ohmic cou- pling. The tunable dot-phonon coupling then allows the crossing of a dissipative quantum phase transition [5,8], and can serve also as a novel spectroscopic tool to measure directly atomic Luttinger parameters. Let us consider cold bosonic atoms with two (hyperfine) ground states a and b (Fig. 1). Atoms in state a form a reservoir of atoms in a superfluid phase, held in a shallow trapping potential V a x. The AQD is formed by trapping atoms in state b in a tightly confining potential V b x produced, e.g., by a focused laser beam induced potential or by a deep optical lattice potential which is seen only by atoms in state b [4]. Within the standard pseudopotential description, the collisional interaction of atoms in the two internal levels ; a;b is described by a set of coupling parameters g 4a h 2 =m with scattering lengths a [9] and atomic mass m. We assume that the reservoir atoms are coupled via a Raman transition to the lowest vibrational state in the AQD, where spontaneous emission is suppressed by a large detuning from the excited elec- tronic states. Thus, following arguments analogous to those in the derivation of the Bose-Hubbard model of cold atoms in an optical lattice [4], we obtain an effective Hamiltonian, H b H ab h 0 g ab Z dxj b xj 2 ^ a x ^ b y ^ b U bb 2 ^ b y ^ b y ^ b ^ b Z dx h ^ a x b x ^ b y H:c:: (1) FIG. 1. Schematic setup of an atomic quantum dot coupled to a superfluid atomic reservoir. The Bose liquid of atoms in state a is confined in a shallow trap V a x. The atom in state b is localized in tightly confining potential V b x. Atoms in states a and b are coupled via a Raman transition with effective Rabi frequency . A large on-site interaction U bb > 0 allows only a single atom in the dot. PRL 94, 040404 (2005) PHYSICAL REVIEW LETTERS week ending 4 FEBRUARY 2005 0031-9007= 05=94(4)=040404(4)$23.00 040404-1 2005 The American Physical Society