Spatial adiabatic passage of massive quantum particles in an optical Lieb lattice

Abstract

By adiabatically manipulating tunneling amplitudes of cold atoms in a periodic potential with a multiple sublattice structure, we are able to coherently transfer atoms from a sublattice to another without populating the intermediate sublattice, which can be regarded as a spatial analogue of stimulated Raman adiabatic passage. A key is the existence of dark eigenstates forming a flat band in a Lieb-type optical lattice. We also successfully observe a matter-wave analogue of Autler-Townes doublet using the same setup. This work shed light on a novel kind of coherent control of cold atoms in optical potentials.Interference of probability amplitudes is one of the most significant properties of quantum mechanics. In the seminal work of an electron double-slit experiment [1], building up of the interference pattern of electron wave function beautifully demonstrated nature of waveparticle duality. Quantum interference has been intensively utilized especially in the field of precision measurement such as superconducting magnetometer [2] and atom interferometry [3], and also lies at the heart of quantum information science.A three-level system is a minimal example in which quantum interference takes place. Most commonly it is considered in a context of laser coupled atomic levels, and the Hamiltonian for a Λ-type system (Fig. 1 (a)) in a rotating frame is written in the formwhere Ω 1 (Ω 2 ) denotes a laser-induced Rabi frequency which couples basis states |A with |B (|A with |C ), and δ 1 (δ 2 ) is the detuning of the corresponding laser 1 (2). A dark state cos θ|B − sin θ|C (tan θ = Ω 1 /Ω 2 ) arises as one of the eigenstate of the Hamiltonian given by Eq.(1) if the Raman resonant condition δ 1 = δ 2 is satisfied. By applying two laser pulses in so-called "counter-intuitive" order so that θ changes form 0 to π/2, the dark states smoothly evolve from |B into |C . This process is well known as Stimulated Raman Adiabatic Passage (STIRAP) [4][5][6], and has been an important technique for robust population transfer between two atomic/molecular states. Natural interests arise for a special case that the states of interest represent a matter wave of a quantum particle and the initial and the final states are spatially well isolated. Such processes, named spatial adiabatic passage (SAP), offer paradoxical "transport without transit" [7,8] where matter waves are transported without populating the intermediate spatial region. Since the concept of SAP was introduced in the context of quantum * Electronic address: taie@scphys.kyoto-u.ac.jp FIG.

Lifetime of flatband states

“…In this sense, the identified mechanism may serve as a baseline estimate on the stability of flatband states. Near-future experimental confirmations in existing platforms are conceivable [6][7][8][10][11][12][13][14][15][16][17][18][19][20][21]. Generalizing the theory to 2D/3D, and including the evolution of dispersive-band components, could further illuminate the interplay of flat and dispersive bands.…”

“…NUMERICAL TEST Figure 2 displays the time evolution for: the initial flatband state (i) partially overlapping with one intersection or (ii) residing in between the two intersections. In both cases we compare the numerically exact evolution in the cross-stitch model (N = 100 unit cells, periodic boundary conditions, averaged over K = 200 realizations) with our analytical prediction (12). We use Gaussian correlations [the integral in (9) can then be solved analytically] with W = 0.5J (C 0 = W 2 /12), = 6a, and δ = 0.…”

“…Flatbands, which may emerge as a consequence of symmetries or finetuning in certain tight-binding Hamiltonians, are characterized by a completely dispersionless single-particle energy spectrum, i.e., the band's energy E(p) is independent of the Bloch state momentum p. Predicted several decades ago [1, 2], they have recently become experimentally accessible in artificial lattice systems, ranging from electronic [3][4][5][6][7][8][9], to atomic [10][11][12] and photonic [13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Preformed pairs in flat Bloch bands

“…There are several avenues where our results could be put to experimental test. In recent years there have been several realizations of flat bands models using optical lattices [73][74][75][76] and more recently the Creutz ladder has been proposed as a workhorse for the study of topological effects in ultracold gases and its implementation seems to be within reach with current experimental tools [43]. The diamond chain has been recently implemented with photonic lattices [77], while excited orbital angular momentum states of ultracold atoms have been proposed as a new venue for implementing the same model [78].…”

Entanglement in Spatial Adiabatic Processes for Interacting Atoms

“…Spatial adiabatic passage (SAP) techniques [8] are specific class of adiabatic methods that allow to manipulate the center-of-mass state of single particles in inhomogeneous potentials. They have been experimentally demonstrated recently [13], making them an attractive quantum state engineering tool. In their first incarnation [14] they were developed as a direct translation of the well-known STIRAP technique in optics [15].…”