Erratum: Direct Observation of Coherent Interorbital Spin-Exchange Dynamics [Phys. Rev. Lett.<b>113</b>, 120402 (2014)]

Cappellini, Giacomo; Mancini, M.; Pagano, Guido; Lombardi, Pietro; Livi, L.; Cumis, Mario Siciliani de; Cancio, P.; Pizzocaro, Marco; Calonico, Davide; Levi, Filippo; Sias, Carlo; Catani, Jacopo; Inguscio, M.; Fallani, Leonardo

doi:10.1103/physrevlett.114.239903

Phys. Rev. Lett.

2015

DOI: 10.1103/physrevlett.114.239903

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Erratum: Direct Observation of Coherent Interorbital Spin-Exchange Dynamics [Phys. Rev. Lett.113, 120402 (2014)]

Giacomo Cappellini¹,

M. Mancini²,

Guido Pagano³

et al.

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Cited by 43 publications

(62 citation statements)

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“…As demonstrated in recent experiments with 173 Yb [32,33], the spin-exchange interaction in these settings can be extremely large, of the order of 5/10 kHz in optical lattices, guaranteeing that the driven interaction strength in our system is considerably larger than typical temperatures. Moreover, the ratio W/t can be tuned via modifying either the optical lattice depth or the trapping in the transverse direction.…”

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confidence: 92%

Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

et al. 2017

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We show how angular momentum conservation can stabilise a symmetry-protected quasitopological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe -spin-orbit coupling and strong inter-orbital interactions -have been experimentally realized over the last two years.PACS numbers: 37.10. Jk, 05.10.Cc, 71.10.Pm Introduction. -The past two decades have witnessed an impressive progress in understanding how to harness quantum systems supporting topological order, one of the ultimate goals being the observation of quasi-particles with non-Abelian statistics -non-Abelian anyons [1][2][3][4][5]. A pivotal role in this search has been the formulation of a model for one-dimensional (1D) p-wave superconductors [6], that supports a symmetry-protected topological phase with Majorana quasi-particles (MQPs) as edge modes. The key element for the stability of such edge modes is the presence of a Z 2 parity symmetry. At the mean-field level, this can be realized via proximityinduced superconductivity in solid-state settings [7][8][9][10][11][12], or via coupling to molecular Bose-Einsten condensates in cold atoms [13]. Remarkably, it is possible to stabilize MQPs even taking fully into account quantum fluctuations by considering canonical settings [14][15][16][17][18], where the parity symmetry emerges via, e.g., engineered pairtunneling between pairs of wires [19][20][21]. However, it is an open challenge to understand whether, in these number-conserving setups, there exist fundamental microscopic symmetries that can serve as a pristine mechanism for the realization of MQPs, that is genuinely distinct from reservoir-induced superconductivity.Here, we show how angular momentum conservation enables the realization of a symmetry-protected quasitopological phase supporting MQPs in one-dimensional number-conserving systems [22]. In particular, we show how a combination of spin-exchange interactions and crossed spin-orbit couplings in orbital Hubbard models (see Fig. 1a-b) naturally gives rise to a Z 2 spin symmetry. This symmetry serves as the enabling tool to realize (1) describes tunneling (Ht), spin-orbit-coupling (Hso), and spin-exchange processes (HW ). In cold atom settings, the spin degree of freedom is represented by different Zeeman states with nuclear spin mF , mF + 1, while the orbital degree of freedom is encoded in different electronic states, 1 S0 and 3 P0. ...

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Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

et al. 2017

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“…Recent theoretical proposal [1] and the subsequent experimental confirmations [2,3] of the socalled orbital Feshbach resonance (OFR) in alkalineearth atoms have opened a new avenue to investigate strongly interacting Fermi gases. A prominent feature of the alkaline-earth atoms, such as Sr [4], Yb [5][6][7], is that there are two clock states, the electronic s-and p-states, both of which have zero electronic angular momentum J = 0. As a result, there is no hyperfine coupling between the electronic and nuclear spins.…”

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confidence: 99%

“…We show how these collective modes are reflected in the density response of the system. [5][6][7], is that there are two clock states, the electronic s-and p-states, both of which have zero electronic angular momentum J = 0. As a result, there is no hyperfine coupling between the electronic and nuclear spins.…”

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confidence: 99%

Collective modes in a two-band superfluid of ultracold alkaline-earth-metal atoms close to an orbital Feshbach resonance

2017

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We discuss the collective modes in an alkaline-earth Fermi gas close to an orbital Feshbach resonance. Unlike the usual Feshbach resonance, the orbital Feshbach resonance in alkaline-earth atoms realizes a two-band superfluid system where the fermionic nature of both the open and the closed channel has to be taken into account. We show that apart from the usual Anderson-Bogoliubov mode which corresponds to the oscillation of total density, there also appears the long-sought Leggett mode corresponding to the oscillation of relative density between the two channels. The existence of the phonon and the Leggett modes and their evolution are discussed in detail. We show how these collective modes are reflected in the density response of the system. [5][6][7], is that there are two clock states, the electronic s-and p-states, both of which have zero electronic angular momentum J = 0. As a result, there is no hyperfine coupling between the electronic and nuclear spins. The inter-atomic interactions which depend (primarily) on the electronic configurations thus become independent of nuclear spins. This realizes the so-called SU (N ) symmetries, where N is the number of nuclear spin components [8][9][10][11][12][13][14][15]. The OFR relies on the atoms residing on both the s and p-states which possess slight different Landé g-factors [16,17], thus allowing tuning by external magnetic field.

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“…1(b)]. This endowsĤ with an additional SU(N ) spin-rotation symmetry, where N can be tuned between 2 and 2I + 1 by choosing the initial state [33][34][35][36][37][38]. Restricted to g,Ĥ is just the sum of spin swaps over all pairs of occupied orbitals and can be diagonalized in terms of irreducible representations of the group of symmetries G = S n × SU(N ).…”

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Realizing exactly solvableSU(N)magnets with thermal atoms

et al. 2016

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We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the S n symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N ) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N ) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.DOI: 10.1103/PhysRevA.93.051601The study of quantum spin models with ultracold atoms [1,2] promises to give crucial insights into a range of equilibrium and nonequilibrium many-body phenomena from quantum spin liquids [3] and many-body localization [4] to quantum quenches [5][6][7] and quantum annealing [8]. While other approaches exist [9][10][11][12], the most common approach taken to implement a quantum spin model with ultracold atoms relies on preparing a Mott insulator in an optical lattice, where the internal states of atoms on each site define the effective spin [1,[13][14][15][16][17][18][19]. Virtual hopping processes to neighboring sites and back then give rise to effective superexchange spin-spin interactions. Since the superexchange interactions are typically very weak ( kHz) [1] (unless the traps are operated near surfaces, which can reduce spacings and increase energy scales [20][21][22]), it is a significant challenge in experimental cold-atom physics to achieve temperatures and decoherence rates low enough to access superexchange-based quantum magnetism.Since ultracold atoms can be prepared in specific internal (i.e., spin) states with extremely high precision, spin temperatures that can be realized are much lower than the experimentally achievable motional temperatures. It is therefore tempting to circumvent the problem of high motional temperature by constructing a spin model in such a way that the motional and spin degrees of freedom are effectively decoupled. We provide a recipe for such a decoupling and hence for realizing spin models with thermal atoms.The first crucial ingredient for implementing such a spin model is to depart from second-order superexchange interactions and use contact interactions to first order [23][24][25][26][27][28][29][30][31][32]. As shown in Fig. 1(a), this can be achieved if all atoms sit in different orbitals of the same anharmonic trap and remain in these orbitals throughout the evolution, which is a good approximation for weak interactions [23][24][25]30,31]. In that case, the occupied orbitals play the role of the sites of the spin Hamiltonian. However, because of high motional temperature in such systems, every run of the experiment typically yields a different set of populated orbitals and hence a diff...

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Erratum: Direct Observation of Coherent Interorbital Spin-Exchange Dynamics [Phys. Rev. Lett.113, 120402 (2014)]

Cited by 43 publications

References 0 publications

Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

Collective modes in a two-band superfluid of ultracold alkaline-earth-metal atoms close to an orbital Feshbach resonance

Realizing exactly solvableSU(N)magnets with thermal atoms

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