We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.
It is shown that by switching a specific time-dependent interaction between a harmonic oscillator and a transmission line ͑a waveguide, an optical fiber, etc.͒ the quantum state of the oscillator can be transferred into that of another oscillator coupled to the distant other end of the line, with a fidelity that is independent of the initial state of both oscillators. For a transfer time T, the fidelity approaches 1 exponentially in ␥T where ␥ is a characteristic damping rate. Hence, a good fidelity is achieved even for a transfer time of a few damping times. Some implementations are discussed.A state transfer between two identical distant systems ͑say, two nodes of a quantum network͒ is a process in which at time t = T the second system obtains the same quantum state that the first one had at time t = 0. The systems between which the state is transferred may include, for example, atoms in a cavity ͓1,2͔ or spin or flux qubits ͓3,4͔. The need for a fast and reliable state transfer in quantum computers and quantum networks is posing questions concerning the limitations in practice and in principle on the speed and reliability of such a communication form ͑in addition to the obvious limitations related to the speed of light͒. These questions were considered mainly ͓3-6͔, though not only ͓7-10͔, in condensed matter systems where the transferred states belong to a finite-dimensional Hilbert space ͑e.g., that of twoor three-level systems and unlike the state of a harmonic oscillator͒.Here we consider a state transfer between two identical harmonic oscillators coupled to opposite ends of a transmission line. We show that by performing a single operation of properly chosen time-dependent switching of the coupling ͓denoted by ␥͑t͔͒ between one of the oscillators and the transmission line, a state transfer is achieved with an arbitrary high fidelity which is independent of the initial states of the two oscillators.We start by analyzing the case where a single oscillator ͑labeled i͒ is coupled to a transmission line with a constant coupling ␥ i . Assuming that ␥ i ͑which also characterizes the damping of the oscillator͒ is much smaller than the oscillator frequency 0 , one is allowed to use the slowly varying envelope, Markov, and rotating-wave approximations. In a frame rotating at the oscillator frequency, the Heisenberg equations of motion are then given by ͑see, e.g., Eqs. ͑7.15͒ and ͑7.18͒ in Ref. ͓12͔͒ da i dt + ␥ i a i = ͱ 2␥ i b i,in ͑t͒, i = 1,2, ͑1͒ and ͱ 2␥ i a i = b i,in ͑t͒ + b i,out ͑t͒. ͑2͒ a i ͑t͒ annihilates a mode of the oscillator i and satisfies ͓a i ͑t͒ , a i † ͑t͔͒ =1. b i,in/out ͑t͒ is an operator related to the incom-ing and outgoing fields in the transmission line by ͓11͔where b i,␣ ͑͒ annihilates a transmission line mode propagating toward ͑for ␣ =in͒ or away from ͑for ␣ = out͒ the oscillator i, and͑1͒ is the line-oscillator coupling strength and thus appears in both the damping term on the right of Eq. ͑1͒ and the driving term on the left. Equation ͑2͒ is a boundary condition matching the value o...
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