Particle delocalization is a common feature of quantum random walks in arbitrary lattices. However, in the typical scenario a particle spreads over multiple sites and its evolution is not directly useful for controlled quantum interferometry, as may be required for technological applications. In this paper we devise a strategy to perfectly split the wave-packet of an incoming particle into two components, each propagating in opposite directions, which reconstruct the shape of the initial wavefunction after a particular time t * . Therefore, a particle in a delta-like initial state becomes exactly delocalized between two distant sites after t * . We find the mathematical conditions to achieve the perfect splitting which are satisfied by viable example Hamiltonians with static sitedependent interaction strengths. Our results pave the way for the generation of peculiar many-body interference patterns in a many-site atomic chain (like the Hanbury Brown and Twiss and quantum Talbot effects) as well as for the distribution of entanglement between remote sites. Thus, as for the case of perfect state transfer, the perfect wave-packet splitting can be a new tool for varied applications.
A toolbox for the quantum simulation of polarons in ultracold atoms is presented. Motivated by the impressive experimental advances in the area of ultracold atomic mixtures, we theoretically study the problem of ultracold atomic impurities immersed in a Bose-Einstein condensate mixture (BEC). The coupling between impurity and BEC gives rise to the formation of polarons whose mutual interaction can be effectively tuned using an external laser driving a quasi-resonant Raman transition between the BEC components. Our scheme allows one to change the effective interactions between polarons in different sites from attractive to zero. This is achieved by simply changing the intensity and the frequency of the two lasers. Such arrangement opens new avenues for the study of strongly correlated condensed matter models in ultracold gases.
Tight binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. How to harness this mobility in a many-site lattice for useful operations is still an open question. We show how effective linear optics-like operations between arbitrary lattice sites can be implemented by a minimal local control which introduces a local impurity in the middle of the lattice. In particular we show how striking is the difference of the two possible correlations with and without the impurity. Our scheme enables the observation of the Hong-Ou-Mandel effect between distant wells without moving them next to each other with, e.g., tweezers. Moreover, we show that a tunable Mach-Zehnder interferometer is implemented adding a step-like potential, and we prove the robustness of our linear optics scheme to interparticle interactions.Linear optical networks are indispensable tools for both fundamental investigations of quantum interference phenomena and for practical applications. Beam splitters acting on two modes enable one to design simple two output interferometers such as the Mach-Zehnder and to observe bosonic behavior of two incident particles in the most striking way through the Hong-Ou-Mandel effect where the probability of one photon in each output is completely suppressed. The same types of effects form the bedrock of linear optical quantum computation [1,2], and of the boson sampling device [3][4][5][6][7]. The recent atomic realization of a controlled beam splitter in a double well potential [8] highlights the importance of atomic linear optics. This, and the recent unprecedented abilities to initialize and measure the positions of individual atoms [9][10][11][12], raise the intriguing question: can we use a many-site lattice for performing arbitrary linear-optics operations? Large lattices are indeed required for many applications, such as boson sampling where the complexity increases dramatically when the number sites is much larger than the number of particles.At a first glance, the realization of arbitrary operations seems improbable, as atoms on a multi-site lattice typically perform a "quantum walk" which is dispersive. This severely limits the observability even of basic linear-optics effects, such as bosonic bunching and/or fermionic anti-bunching, as the particles quickly spread out between multiple modes [9,10,[13][14][15][16][17][18][19]. In fact, such phenomena cannot be observed unless the particles are nearest neighbors or in the same site [18], even in the interacting case [9,10]. Obviously a new methodology is required in an atomic multi-site lattice for neat two mode demonstrations of such effects (as with two photons on a beam splitter [20] or matter waves [21]).Motivated as above we show (i) how to implement remote linear optics via the dynamics of trapped neutral atoms interacting via the Bose-Hubbard Hamiltonian; (ii) how to improve the efficiency of our scheme by introducing a minimal engineering of the couplings. Unlike ...
Tight-binding lattice models allow the creation of bound composite objects which, in the strong-interacting regime, are protected against dissociation. We show that a local impurity in the lattice potential can generate a coherent split of an incoming bound particle wave-packet which consequently produces a NOON state between the endpoints. This is non trivial because when finite lattices are involved, edge-localization effects make their use for non-classical state generation and information transfer challenging. We derive an effective model to describe the propagation of bound particles in a Bose-Hubbard chain. We introduce local impurities in the lattice potential to inhibit localization effects and to split the propagating bound particle, thus enabling the generation of distant NOON states. We analyze how minimal engineering transfer schemes improve the transfer fidelity and we quantify the robustness to typical decoherence effects in optical lattice implementations. Our scheme potentially has an impact on quantum-enhanced atomic interferometry in a lattice.
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