Abstract
We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state through a Raman scheme. The coupling between these two types of atoms (trapped and free) turns out to be similar to that describing light–matter interaction within the rotating-wave approximation, the role of matter and photons being played by the trapped and free atoms, respectively. We explain in particular how to observe phenomena arising from the collective spontaneous emission of atomic and harmonic oscillator samples, such as superradiance and directional emission. We also show how the same setup can simulate Bose–Hubbard Hamiltonians with extended hopping as well as Ising models with long-range interactions. We believe that this system can be realized with state of the art technology.
Highlights
We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems
We have studied a model consisting of atoms trapped in an optical lattice, which are coherently driven to a non-trapped state through a Raman scheme having detuning with respect to the atomic transition, relative wave vector between the Raman lasers kL, and two-photon Rabi frequency
These are the main results that we have found: (2) We have first deduced the Hamiltonian of the system, showing that it is equivalent to that of a collection of harmonic oscillators or two-level systems for non-interacting atoms and hard-core bosons, respectively, interacting with a common radiation field consisting of massive particles
Summary
Our starting point is the Hamiltonian of the system in second quantization [26]. We will denote by |a and |b the trapped and free atomic states, respectively As for the second limit, we assume that the on-site repulsive atom–atom interaction is the dominant energy scale, and the trapped atoms behave as hard-core bosons in the collisional blockade regime, which prevents the presence of two atoms in the same lattice site [25]; this means that the spectrum of a†j aj can be restricted to the first two states {|0 j, |1 j}, having 0 or 1 atom at site j, and the boson operators {a†j , aj} can be changed by spin-like ladder operators {σj†, σj} = {|1 j 0|, |0 j 1|} In this second limit, the Hamiltonian reads gk ei kt−i(k−kL)·rj σjb†k + H.c. Hamiltonians (3) and (5) show explicitly how this system mimics the dynamics of collections of harmonic oscillators or atoms, respectively, interacting with a common radiation field. That to satisfy that the trapped atoms are within the first Bloch band, it is required that ω0 ,
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