Toolbox for linear optics in a one-dimensional lattice via minimal control

Abstract

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 ...

NOON states via a quantum walk of bound particles

“…ting [37]. Indeed, the extra barrier favors the splitting of the propagating bound particle wave-packet into a transmitted and reflected component.…”

“…1 and discussed in [37]. We set the value β ′ = J 2 /4U for the edge fields µ j = −β ′ (δ j,1 + δ j,L ) to remove edge locking.…”

“…(2) is valid in the regime U/J ≫ 1, we analyze deviations from the theoretical value of β ′ , by evaluating the dynamics with exact diagonalization techniques as in [37,38]. Once initialized the system in |ψ(0) ∝ (a † 1 ) 2 |0 we numerically find the value of β ′ that maximize the probability to find, at the transfer time t * ∼ L/J eff , the bound particle in the last site of the chain P LL (t * ).…”

“…When distant sites are involved, a balanced beam splitter transformation can be obtained via the particle dynamics by introducing suitable impurities in the lattice potential. These impurities generate a coherent splitting of the wave-packet of propagating particles which enables high-efficiency effective linear optical operations between remote sites of finite lattices [37,38]. Even without the onsite interaction, peculiar quantum interference effects enable the production of non-classical states, namely two particle NOON states, via the celebrated Hong-Ou-Mandel effect [37,38].…”

“…These impurities generate a coherent splitting of the wave-packet of propagating particles which enables high-efficiency effective linear optical operations between remote sites of finite lattices [37,38]. Even without the onsite interaction, peculiar quantum interference effects enable the production of non-classical states, namely two particle NOON states, via the celebrated Hong-Ou-Mandel effect [37,38]. Being a linear-optical effect, the efficiency of this protocol is maximized when the atom-atom interaction is kept in the weak coupling regime.…”