Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on "discrete time crystals", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts.

1 aElse, Dominic, V.1 aMonroe, Christopher1 aNayak, Chetan1 aYao, Norman, Y. uhttps://arxiv.org/abs/1905.1323201858nas a2200169 4500008004100000245004400041210004400085520137000129100002401499700002201523700002101545700002301566700001801589700002001607700002401627856003701651 2018 eng d00aVerified Quantum Information Scrambling0 aVerified Quantum Information Scrambling3 aQuantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically ∼80%, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

1 aLandsman, Kevin, A.1 aFiggatt, Caroline1 aSchuster, Thomas1 aLinke, Norbert, M.1 aYoshida, Beni1 aYao, Norman, Y.1 aMonroe, Christopher uhttps://arxiv.org/abs/1806.0280701527nas a2200181 4500008004100000245006900041210006900110260001500179300001100194490000700205520098100212100002001193700002401213700002301237700002201260700002501282856003801307 2015 eng d00aBilayer fractional quantum Hall states with ultracold dysprosium0 aBilayer fractional quantum Hall states with ultracold dysprosium c2015/09/10 a0336090 v923 a We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hardcore bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the \nu = 1/2 Laughlin state. Thinking of spin-1 particles as two-component hardcore bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed. 1 aYao, Norman, Y.1 aBennett, Steven, D.1 aLaumann, Chris, R.1 aLev, Benjamin, L.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1505.03099v101270nas a2200193 4500008004100000245005700041210005700098260001500155300001100170490000700181520071900188100002700907700002000934700002100954700001700975700002200992700002501014856003701039 2015 eng d00aFractional Quantum Hall States of Rydberg Polaritons0 aFractional Quantum Hall States of Rydberg Polaritons c2015/03/31 a0338380 v913 a We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. 1 aMaghrebi, Mohammad, F.1 aYao, Norman, Y.1 aHafezi, Mohammad1 aPohl, Thomas1 aFirstenberg, Ofer1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1411.6624v102029nas a2200241 4500008004100000245006600041210006500107260001400172490000800186520133800194100002601532700001801558700002301576700001201599700002201611700002101633700002001654700002301674700001201697700002101709700002001730856003701750 2014 eng d00aMany-body dynamics of dipolar molecules in an optical lattice0 aManybody dynamics of dipolar molecules in an optical lattice c2014/11/70 v1133 a Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the dipolar interaction strength, and we demonstrate that the many-body dynamics extends well beyond a nearest-neighbor or mean-field picture, and cannot be quantitatively described using previously available theoretical tools. We develop a novel cluster expansion technique and demonstrate that our theoretical method accurately captures the measured dependence of the spin dynamics on molecule number and on the dipolar interaction strength. In the spirit of quantum simulation, this agreement simultaneously benchmarks the new theoretical method and verifies our microscopic understanding of the experiment. Our findings pave the way for numerous applications in quantum information science, metrology, and condensed matter physics. 1 aHazzard, Kaden, R. A.1 aGadway, Bryce1 aFoss-Feig, Michael1 aYan, Bo1 aMoses, Steven, A.1 aCovey, Jacob, P.1 aYao, Norman, Y.1 aLukin, Mikhail, D.1 aYe, Jun1 aJin, Deborah, S.1 aRey, Ana, Maria uhttp://arxiv.org/abs/1402.2354v101262nas a2200193 4500008004100000245009300041210006900134260001400203490000700217520064800224100002200872700002000894700002500914700002000939700002400959700002100983700002701004856003701031 2013 eng d00aControllable quantum spin glasses with magnetic impurities embedded in quantum solids 0 aControllable quantum spin glasses with magnetic impurities embed c2013/7/240 v883 a Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. 1 aLemeshko, Mikhail1 aYao, Norman, Y.1 aGorshkov, Alexey, V.1 aWeimer, Hendrik1 aBennett, Steven, D.1 aMomose, Takamasa1 aGopalakrishnan, Sarang uhttp://arxiv.org/abs/1307.1130v101995nas a2200205 4500008004100000245005100041210005100092260001300143490000700156520142000163100002001583700001901603700002301622700002401645700001801669700002301687700001701710700002501727856003701752 2013 eng d00aQuantum Logic between Remote Quantum Registers0 aQuantum Logic between Remote Quantum Registers c2013/2/60 v873 a We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. 1 aYao, Norman, Y.1 aGong, Zhe-Xuan1 aLaumann, Chris, R.1 aBennett, Steven, D.1 aDuan, L., -M.1 aLukin, Mikhail, D.1 aJiang, Liang1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1206.0014v101351nas a2200181 4500008004100000245006100041210006100102260001400163490000800177520081800185100002001003700002501023700002301048700002601071700001201097700002301109856003701132 2013 eng d00aRealizing Fractional Chern Insulators with Dipolar Spins0 aRealizing Fractional Chern Insulators with Dipolar Spins c2013/4/290 v1103 a Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications. 1 aYao, Norman, Y.1 aGorshkov, Alexey, V.1 aLaumann, Chris, R.1 aLĂ¤uchli, Andreas, M.1 aYe, Jun1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1212.4839v101443nas a2200217 4500008004100000245007500041210006900116260001400185300000900199490000600208520080900214100002001023700002301043700002501066700002001091700001701111700001901128700001801147700002301165856003701188 2013 eng d00aTopologically Protected Quantum State Transfer in a Chiral Spin Liquid0 aTopologically Protected Quantum State Transfer in a Chiral Spin c2013/3/12 a15850 v43 a Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. 1 aYao, Norman, Y.1 aLaumann, Chris, R.1 aGorshkov, Alexey, V.1 aWeimer, Hendrik1 aJiang, Liang1 aCirac, Ignacio1 aZoller, Peter1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1110.3788v101927nas a2200205 4500008004100000245009400041210006900135260001400204300000800218490000600226520130900232100002001541700001701561700002501578700002201603700001701625700001901642700002301661856003701684 2012 eng d00aScalable Architecture for a Room Temperature Solid-State Quantum Information Processor 0 aScalable Architecture for a Room Temperature SolidState Quantum c2012/4/24 a8000 v33 a The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Much progress has been made towards this goal. Indeed, quantum operations have been demonstrated on several trapped ion qubits, and other solid-state systems are approaching similar levels of control. Extending these techniques to achieve fault-tolerant operations in larger systems with more qubits remains an extremely challenging goal, in part, due to the substantial technical complexity of current implementations. Here, we propose and analyze an architecture for a scalable, solid-state quantum information processor capable of operating at or near room temperature. The architecture is applicable to realistic conditions, which include disorder and relevant decoherence mechanisms, and includes a hierarchy of control at successive length scales. Our approach is based upon recent experimental advances involving Nitrogen-Vacancy color centers in diamond and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems. Additionally, the proposed architecture may greatly alleviate the stringent constraints, currently limiting the realization of scalable quantum processors. 1 aYao, Norman, Y.1 aJiang, Liang1 aGorshkov, Alexey, V.1 aMaurer, Peter, C.1 aGiedke, Geza1 aCirac, Ignacio1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1012.2864v101339nas a2200193 4500008004100000245005300041210005300094260001500147490000800162520078600170100002000956700002300976700002500999700002401024700001901048700001801067700002301085856003701108 2012 eng d00aTopological Flat Bands from Dipolar Spin Systems0 aTopological Flat Bands from Dipolar Spin Systems c2012/12/260 v1093 a We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. 1 aYao, Norman, Y.1 aLaumann, Chris, R.1 aGorshkov, Alexey, V.1 aBennett, Steven, D.1 aDemler, Eugene1 aZoller, Peter1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1207.4479v301404nas a2200193 4500008004100000245006800041210006800109260001400177490000800191520083700199100002001036700001701056700002501073700001901098700001501117700001801132700002301150856003701173 2011 eng d00aRobust Quantum State Transfer in Random Unpolarized Spin Chains0 aRobust Quantum State Transfer in Random Unpolarized Spin Chains c2011/1/270 v1063 a We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. 1 aYao, Norman, Y.1 aJiang, Liang1 aGorshkov, Alexey, V.1 aGong, Zhe-Xuan1 aZhai, Alex1 aDuan, L., -M.1 aLukin, Mikhail, D. uhttp://arxiv.org/abs/1011.2762v2