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arXiv:1503.07466 · Physical Review A

Adiabatic cooling of bosons in lattices to magnetically ordered quantum states

Johannes Schachenmayer, David Weld, Hirokazu Miyake, Georgios A. Siviloglou, Wolfgang Ketterle, Andrew J. Daley

Published Oct 14, 2015• 27 citations
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Abstract

We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an $xy$-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with $xy$-ferromagnetic order if the ramp crosses to regimes where the ground state is a $z$ ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies.

DOI
10.1103/physreva.92.041602

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We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an xyxyxy-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with xyxyxy-ferromagnetic order if the ramp crosses to regimes where the ground state is a zzz ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies.
Abstract We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and their robustness to decoherence is quantified by computing the quantum Fisher information (QFI) of final states. We identify that the generation of useful entanglement should in general be more robust to heating than it would be implied by the state fidelity, with corresponding implications for practical applications.
The microscopic control available over cold atoms in optical lattices has opened new opportunities to study the properties of quantum spin models. While a lot of attention is focused on experimentally realizing ground or thermal states via adiabatic loading, it would often be more straightforward to prepare specific simple product states and to probe the properties of interacting spins by observing their dynamics. We explore this possibility for spin-1/2 and spin-1 models that can be realized with bosons in optical lattices, and which exhibit XY\mathit{XY}XY-ferromagnetic (or counterflow spin-superfluid) phases. We consider the dynamics of initial spin-rotated states corresponding to a mean-field version of the phases of interest. Using matrix product state methods in one dimension, we compute both nonequilibrium dynamics and ground and thermal states for these systems. We compare and contrast their behavior in terms of correlation functions and induced spin currents, which should be directly observable with current experimental techniques. We find that although spin correlations decay substantially at large distances and on long timescales, for induction of spin currents, the rotated states behave similarly to the ground states on experimentally observable timescales.
The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N\'eel temperature. However, reaching this temperature in the laboratory has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the SU(2)\text{SU}(2)SU(2) symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the SU(2)\text{SU}(2)SU(2) symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low-temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low-temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard model.
We analyze the effects of adiabatic ramping of optical lattices on the temperature of spin-1 bosons in a homogeneous lattice. Using mean-field theory, we present the isentropes in the temperature-interaction strength (T,U0T,{U}_{0}T,U0​) plane for ferromagnetic, antiferromagnetic, and zero spin couplings. Following the isentropic lines, temperature changes can be determined during adiabatic loading of current experiments. We show that the heating-cooling separatrix lies on the superfluid-Mott phase boundary with cooling occurring within the superfluid and heating in the Mott insulator and quantify the effects of spin coupling on the heating rate. We find that the mean-field isentropes for low initial entropy terminate at the superfluid--Mott-insulator phase boundary.
We study the ground states of two-dimensional lattice bosons in an artificial gauge field. Using state-of-the-art density matrix renormalization group (DMRG) simulations we obtain the zero-temperature phase diagram for hard-core bosons at densities nb{n}_{b}nb​ with flux ${n}_{\ensuremath{\phi}}$ per unit cell, which determines a filling $\ensuremath{\nu}={n}_{b}/{n}_{\ensuremath{\phi}}$. We find the bosonic Jain sequence $[\ensuremath{\nu}=p/(p+1)]$ states, in particular, a bosonic integer quantum Hall phase at $\ensuremath{\nu}=2$, are fairly robust in the hard-core boson limit, In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation, beginning from independent chains, and ramping up interchain couplings. Using time-dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Our proposal only utilizes existing experimental capabilities.
Quantum many-body phases offer unique properties and emergent phenomena, making them an active area of research. A promising approach for their experimental realization in model systems is to adiabatically follow the ground state of a quantum Hamiltonian from a product state of isolated particles to one that is strongly-correlated. Such protocols are relevant also more broadly in coherent quantum annealing and adiabatic quantum computing. Here we explore one such protocol in a system of ultracold atoms in an optical lattice. A fully magnetized state is connected to a correlated zero-magnetization state (an xy-ferromagnet) by a many-body spin rotation, realized by sweeping the detuning and power of a microwave field. The efficiency is characterized by applying a reverse sweep with a variable relative phase. We restore up to 50% of the original magnetization independent of the relative phase, evidence for the formation of correlations. The protocol is limited by the many-body gap of the final state, which is inversely proportional to system size, and technical noise. Our experimental and theoretical studies highlight the potential and challenges for adiabatic preparation protocols to prepare many-body eigenstates of spin Hamiltonians.