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arXiv:1601.00500 · Journal of Physics B Atomic Molecular and Optical Physics

Orbital optical lattices with bosons

T Kock, C Hippler, A Ewerbeck, A Hemmerich

Published Jan 25, 2016• 44 citations

Abstract

Abstract This article provides a synopsis of our recent experimental work exploring Bose–Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalization process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th bands can be tuned such that two inequivalent energetically degenerate energy minima arise at the X ± -points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Γ-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.

DOI: 10.1088/0953-4075/49/4/042001

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Abstract This article provides a synopsis of our recent experimental work exploring Bose–Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalization process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th bands can be tuned such that two inequivalent energetically degenerate energy minima arise at the X ± -points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Γ-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.

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Since the first experimental realization of Bose-Einstein condensates in a spin-orbit-coupled Zeeman lattice, a wide range of applications have been found in these systems. Here, we systematically study the ground-state phase diagram of the systems. The spin-orbit-coupled Zeeman lattice generates multiple energy minima in the lowest Bloch band. These minima may locate at Brillouin-zone edges and center, or inside the Brillouin zone. Interacting atoms condensing into these minima constitute ground-state quantum phases. Among these phases, the band-edge condensation states have no analog in either spin-orbit-coupled homogeneous systems or lattice systems without the spin-orbit coupling. They exist in a very broad parameter regime of the spin-orbit-coupled Zeeman lattice system. We address superfluidity of the band-edge states by analyzing their elementary excitations and superfluid fraction.

We propose and experimentally explore a method for realizing frustrated lattice models using a Bose-Einstein condensate held in an optical square lattice. A small lattice distortion opens up an energy gap such the lowest band splits into two. Along the edge of the first Brillouin zone for both bands a nearly flat energy-momentum dispersion is realized. For the excited band a highly degenerate energy minimum arises. By loading ultracold atoms into the excited band, a classically frustrated

XY

model is formed, describing rotors on a square lattice with competing nearest and next nearest tunnelling couplings. Our experimental optical lattice provides a regime, where a fully coherent Bose-Einstein condensate is observed, and a regime where frustration is expected. If we adiabatically tune from the condensate regime to the regime of frustration, the momentum spectra shows a complete loss of coherence. Upon slowly tuning back to the condensate regime, coherence is largely restored. Good agreement with model calculations is obtained.

We explore the properties of bosonic atoms loaded into the d bands of an isotropic square optical lattice. Following the recent experimental success reported in Zhai et al (2013 Phys. Rev. A 87 063638 ), in which populating d bands with a 99 fidelity was demonstrated, we present a theoretical study of the possible phases that can appear in this system. Using the Gutzwiller ansatz for the three d band orbitals we map the boundaries of the Mott insulating phases. For not too large occupation, two of the orbitals are predominantly occupied, while the third, of a slightly higher energy, remains almost unpopulated. In this regime, in the superfluid phase we find the formation of a vortex lattice, where the vortices come in vortex/anti-vortex pairs with two pairs locked to every site. Due to the orientation of the vortices time-reversal symmetry is spontaneously broken. This state also breaks a discrete -symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We argue that the corresponding two dimensional phase diagram should be rich with several different phases. We also explain how to generate anti-symmetric spin interactions that can give rise to novel effects like spin canting.

Ultracold neutral atoms in higher bands of an optical lattice provide a natural avenue to emulate orbital physics in solid state materials. Here, we report the realization of 87Rb Bose–Einstein condensates in the fourth and seventh Bloch bands of a hexagonal boron-nitride optical lattice, exhibiting remarkably long coherence time through active cooling. Using band mapping spectroscopy, we observe that atoms condensed at the energy minimum of Γ point (K 1 and K 2 points) in the fourth (seventh) band as sharp Bragg peaks. The lifetime for the condensate in the fourth (seventh) band is about 57.6 (4.8) ms, and the phase coherence of atoms in the fourth band persists for a long time larger than 110 ms. Our work thus offers great promise for studying unconventional bosonic superfluidity of neutral atoms in higher bands of optical lattices.

Abstract Quantum gas systems provide a unique experimental platform to study the crossover between Bose–Einstein condensed molecular pairs and Bardeen–Cooper–Schrieffer superfluidity. The few studies in optical lattices have so far focused on the case when only the lowest Bloch band is populated, thus excluding orbital degrees of freedom. Here we demonstrate the preparation of ultracold Feshbach molecules of fermionic atoms in the second Bloch band of an optical square lattice. We cover a wide range of interaction strengths, including the regime of unitarity in the middle of the crossover. Binding energies and band relaxation dynamics are measured by means of a method resembling mass spectrometry. We find that the longest lifetimes arise for strongly interacting Feshbach molecules at the onset of unitarity. In the case of strong confinement in a deep lattice potential, we observe bound dimers also for negative values of the scattering length, extending previous findings for molecules in the lowest band.