Session J4: Quantum Magnetism and Spin Ensembles

Non-local propagation of correlations in long-range interacting quantum systems

The maximum speed with which information can propagate in a many body quantum system can dictate how demanding the system is to describe numerically and also how quickly disparate sites can become correlated. While these kinds of phenomena may be difficult or even impossible for classical computers to describe, trapped ions provide an excellent platform for investigating this rich quantum many-body physics. Using single-site resolved state-dependent imaging, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For varying interaction ranges, we extract the shape of the ``light'' cone and measure the velocity with which correlations propagate through the system. In many cases, we find increasing propagation velocities, which violate the prediction for short-range interactions and, in one instance, cannot be explained by any existing theory [1]. Our results show that even for modest system sizes, trapped ion quantum simulators are well poised to study complex many-body physics which are intractable to classical methods. \\[4pt] [1] P. Richerme, et al., arXiv:1401.5088   

Observation of entanglement propagation in a quantum many-body system

The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is valid for short-range interactions. Our results will allow experimental studies of a wide range of phenomena and represent a first step towards a new quantum-optical regime with on-demand quasiparticles with tunable non-linear interactions.   

Direct Observation of SU(N) Orbital Magnetism

SU(N) symmetry in matter is predicted to give rise to exotic topological states of matter. In atomic systems such symmetry can occur when the nuclear spin plays no role in the inter-atomic interactions. Ultracold alkaline earth fermionic atoms are expected to obey such symmetry, with the nuclear spin nearly completely decoupled from the electronic angular momentum in the long-lived states. Hence the nuclear spin matters only in quantum statistics, but not in the electronic interaction strength. However, only indirect evidence has been found until recently. Here we use $^{\mathrm{87}}$Sr and directly show the SU(10) symmetry associated with the 10 nuclear spin states. We directly probe the interactions using Ramsey spectroscopy under different magnetic fields and temperatures. We measure the density-dependent frequency shifts and the evolution of atomic coherence under different population distributions of nuclear spin levels. Our measurements fully determine all eight interaction parameters associated with the nuclear spin symmetry/antisymmetry and the spatial and electronic degrees of freedom. These parameters are determined using a many-body spin model for the spin-orbital dynamics and an analytic relation between the s-wave and p-wave scattering lengths.   

Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System

Trapped-ion quantum simulators are a promising candidate for exploring quantum-many-body physics, such as quantum magnetism, that are difficult to examine in condensed-matter experiments or using classical simulation. We demonstrate a coherent imaging spectroscopic technique to validate a quantum simulation [1]. In this work, we study fully-connected transverse Ising models with a chain of up to 18 $^{171}$Yb$^+$ ions. Here, We resolve the state of each spin by collecting the spin-dependent fluorescence on a camera in order to map the complete energy spectrum and fully characterize the spin-spin couplings, while also engineering entangled states and measuring the critical gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators.\\[4pt] [1] C. Senko, et al, arXiv:1401.5751 (2014).   

Using Spin Dephasing for Mode Thermometry in a 2D Trapped-Ion Crystal

Crystals of hundreds of ions confined in Penning traps allow for studies of large quantum systems in a two-dimensional geometry. The transverse ``drumhead" modes of our 2D crystal along with the valence electron spin of the trapped $^9$Be$^+$ serve as a resource for generating spin-motion and spin-spin entanglement. Applying a spin-dependent optical dipole force to a macroscopic spin superposition, we determine the absolute temperature of a single drumhead mode by directly measuring spin dephasing induced by thermal fluctuations of the motion. This technique does not rely on resolved-sideband transitions and is applicable over a large range of mode temperatures. Furthermore, by measuring the spin distribution directly, we distinguish between coherent and thermal mode occupation. Trapped ions are extremely sensitive to small external forces ($\sim$1 yN), and we will discuss extensions of this technique for use in spectroscopy and ion trap characterization.   

Ultracold polar molecules as a quantum simulator

One of the main goals of quantum simulation is to experimentally realize tunable quantum systems as a way to gain insight into strongly correlated many-body phenomena. We have taken the first steps toward this goal in our system of ultracold polar KRb molecules. By encoding spin in rotational states, we have observed spin exchanges of molecules confined in a deep three-dimensional optical lattice. The interactions manifest as a density dependent decay of the spin coherence of the system. In addition, the spin contrast oscillates, with frequency components consistent with the dipolar interaction energies. We vary the interaction strength by using two different pairs of rotational states, and find the decay and oscillations to be roughly twice as fast in the case of stronger interactions. Our experiments are developing in tandem with new theory techniques to describe far-from-equilibrium, long-range interacting systems. In this way, our experiments have led to the development of improved theoretical tools which can be applied to other systems and motivate further experiments on strongly correlated quantum systems. For example, higher lattice fillings in our experiment could enable the study of transport of excitations in an out-of-equilibrium, long-range interacting system.   

Experimental Test of Quantum Jarzynski Equality with a Trapped Ion

We report an experimental test of the Quantum Jarzynski Equality with a single trapped Yb171$+$ ion. The Jarzynski Equality connects work done on the system even through a non-equilibrium process to the free energy difference of the corresponding equilibrium states before and after the process [1]. While many experimental tests of Jarzynski equality have been performed in classical regime, the verification of the quantum version has not yet been fully demonstrated due to experimental challenges required for the test [2]. In our experiment, we apply a laser induced force on a single Yb171$+$ ion trapped in harmonic potential. The Hamiltonian in our realization is same to that of a stretched rubber ring which has been used for the test of classical Jarzynski equality. We vary the speed of this force from adiabatic to far from equilibrium way, and observe the experimental results are in agreement with the expectations from the equality. \\[4pt] [1] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).\\[0pt] [2] G. Huber, F. Schmidt-Kaler, S. Deffner and E. Lutz, Phys. Rev. Lett. 101, 070403 (2008).   

Quantum Simulation of the Majorana Equation with a Trapped Ion

We report on the experimental quantum simulation of symmetry operations such as parity, charge conjugation and time reversal with a trapped ion [1]. In particular, we focus on the realization of anti-unitary operation including complex conjugate as well as time reversal operation in the context of Majorana Equation. It is still unsettled whether a particle described by Majorana equation would exist in nature. Generally, quantum operation is unitary and it is considered to be impossible to implement anti-unitary operation in quantum system. We experimentally study the interesting various phenomena in Majorana equation with a single $^{171}Yb^{+}$ ion based on the proposal of Ref [1]. Quantum simulation may eventually provide a solution to a certain complex problem that is intractable with classical computation. In our study, we explore the other aspect of quantum simulation, where it brings pure theoretical or imaginary concepts to the table top experiment. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts. [1] J. Casanova, et al., Phys. Rev. X, 1, 021018 (2011)   

Certified quantum non-demolition measurement of atomic spins

We report certified quantum non-demolition (QND) measurement of atomic spins via paramagnetic Faraday rotation, recently used to demonstrate spin squeezing in an optical magnetometer [Phys. Rev. Lett. 109, 253605 (2012)]. We apply rigorous criteria, originally developed for continuous variable experiments in optics [Nature 396 537 (1998)] and which we have extended to describe measurements of material systems [New J. Phys. 14, 085021 (2012)], to distinguish QND from similar non-classical measurements. We observe quantum state preparation (QSP) and information-damage trade-off (IDT) beyond their classical limits by seven and twelve standard deviations, respectively [Nat. Phot. 7, 517 (2013)].   

Eigenstate-Assisted Longitudinal Quantum State Transfer and Qubit Storage in Photonic and Spin Lattices

Coherent transport of quantum information between distant nodes plays a role of paramount importance for developing fair quantum computing technologies. In that vein, in this contribution we propose a novel photonic lattice system allowing the perfect transmission of photon encoded quantum information. The basic idea is to use the stationary nature of the associated eigenstates in order to transfer quantum states over long distances with unit fidelity. The proposed system consists of an array of evanescently coupled waveguides obeying a parabolic law distribution for the coupling strength between neighboring elements. In such an optical system, the eigenstates are readily excited provided single sites are fed with single photons. After the eigenstates have been excited, they propagate for very long distances without any distortion. Once the eigenstate has reached the desired distance, it is transformed into a single-site state simetrically residing on the oposite site of the array, performing so a perfect transfer of the initial state. Using these same principles we demonstrated the possibility of storage qubit in spin chains by exploiting the intrinsic time-invariance of the system eigenstates.