Microscopic observation of magnon bound states and their dynamics

Abstract

More than eighty years ago, H. Bethe pointed out the existence of bound states of elementary spin waves in one-dimensional quantum magnets [1]. To date, identifying signatures of such magnon bound states has remained a subject of intense theoretical research [2][3][4][5] while their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting to reveal such bound states by tracking the spin dynamics after a local quantum quench [6] with single-spin and singlesite resolution [7,8]. Here we report on the direct observation of two-magnon bound states using in-situ correlation measurements in a one-dimensional Heisenberg spin chain realized with ultracold bosonic atoms in an optical lattice. We observe the quantum walk of free and bound magnon states through time-resolved measurements of the two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single magnon excitations. In our measurements, we also determine the decay time of bound magnons, which is most likely limited by scattering on thermal fluctuations in the system. Our results open a new pathway for studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.The study of non-equilibrium processes in quantum spin models can provide fundamental insight into elementary aspects of magnetism. Magnons are the basic quasiparticle exitations around the ground state of ferromagnets and govern their low temperature physics [9,10]. Due to the ferromagnetic interaction, two spin excitations can remain bound together, forming a so-called twomagnon bound state [1,9,11]. In one and two dimensions, bound states exist for all center of mass momenta, which prohibits the description of low energy properties in terms of free magnon states [9]. In the classical limit, magnon bound states can be regarded as the basic building blocks of magnetic solitons [12,13]. Next to these fundamental aspects, the study of non-equilibrium dynamics in quantum spin chains is also important for a variety of applications. The evolution of two localized spin excitations realizes an interacting quantum walk [14,15] in the spin domain, which can be a versatile tool for the study of complex many-body systems [16]. It is also of importance in the context of quantum information [17], where transport properties in a one-dimensional chain of qubits can be strongly influenced by magnon bound states [18].The spin-1/2 Heisenberg model is one of the foundational models for interacting quantum spins. This model could be solved analytically in one dimension in the early 1930's by H. Bethe using a systematic Ansatz for the form of the eigenvectors [1]. Later, the Bethe Ansatz proved to be far more general and allowed for solving many more one-dimensional models, such as the Lieb-Liniger or the fermionic Hubbard model [20], and recent, powerful extensions include the investigation of the dynamics * Electronic address: takeshi.fukuhara@mpq....

Nonperturbative expression for the transmission through a leaky chiral edge mode

“…Although a purely 1d system is not experimentally accessible (with the exception, perhaps, of cold atoms [29]), there have been numerous theoretical studies of disordered 1d system in relation to the Anderson localization. Though not present in purely 1d system, the universal fluctuation of conductance can be computed from the disorder averaged moments of conductance [30,31].…”

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

“…Once in the Mott insulating phase, the system can be initialized via single site addressing in a state with a few localised particles, and the dynamics of a single traveling particle [11] and of two (interacting) particles [9,10] can be observed. State preparation fidelity is around 98% while single atom detection is possible with efficiency around 99% [50,51].…”

“…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.…”

“…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]).…”

Quantum logic using correlated one-dimensional quantum walks

“…4 Experimentally, QWs have been implemented using a wide array of platforms, including photonics, [5][6][7][8][9][10][11][12] trapped ions, 13,14 and ultra-cold atoms. [15][16][17] The current degree of experimental control of these systems is remarkable: it is possible to prepare an initial state with single-site and single-particle resolution, to control almost every aspect of the lattice potential, and to directly monitor the evolving wave function. Early experiments demonstrated the behavior of single-particle QWs; however, these dynamics can be desribed by classical wave equations (indeed, some of these experiments were performed with coherent light) [5][6][7]9 ), and thus cannot display non-classical features.…”