The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields [1]. Generating these phases in an engineered system could provide deeper insight into their nature and the potential for harnessing their unique properties [2][3][4][5][6][7]. However, concurrently bringing together the main ingredients for realizing manybody phenomena in a single experimental platform is a major challenge. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall (FQH) phenomena [8, 9]. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions via the creation of photonvacancies, or "holes", which circulate in the opposite direction. The combination of these key elements results in chiral groundstate currents, the first direct measurement of persistent currents in low-lying eigenstates of strongly interacting bosons. The observation of chiral currents at such a small scale is interesting and suggests that the rich many-body physics could survive to smaller scales. We also motivate the feasibility of creating FQH states with near future superconducting technologies. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons and highlight a path toward realization of bosonic FQH states.It is commonly observed that when the number of particles in a system increases, complex phases can emerge which were absent in the system when it had fewer particles, i.e. the "more is different" [10]. This observation drives experimental efforts in synthetic quantum systems, where the primary goal is to engineer and utilize these emerging phases. However, it has generally been overlooked that these sought-after phases can only emerge from simultaneous realization and control of particle numbers, real-space arrangements, external fields, particle interactions, state preparation, and quantum measurement. The simultaneous realization of all these ingredients makes synthesizing many-body phases a holistic task, and hence constitutes a major experimental challenge. Engineering these factors, in particular synthesizing magnetic fields, have been performed in several platforms [4,[11][12][13][14][15][16][17][18][19]. However, these ingredients have not been jointly realized in any system thus far. To provide a tangible framework, we discuss realization of these key elements in the context of quantum Hall physics, and show when these ingredients come together they can construct a basic building block for creating FQH states.The FQH states are commonly studied in 2-dimensional electron gases, a fermionic condensed matter system [8, 9]. However, many of the recent advancem...
Recent progress in nanoscale quantum optics and superconducting qubits has made the creation of strongly correlated, and even topologically ordered, states of photons a real possibility. Many of these states are gapped and exhibit anyon excitations, which could be used for a robust form of quantum information processing. However, while numerous qubit array proposals exist to engineer the Hamiltonian for these systems, the question of how to stabilize the many-body ground state of these photonic quantum simulators against photon losses remains largely unanswered. We here propose a simple mechanism which achieves this goal for abelian and non-abelian fractional quantum Hall states of light. Our construction uses a uniform two-photon drive field to couple the qubits of the primary lattice with an auxiliary "shadow" lattice, composed of qubits with a much faster loss rate than the qubits of the primary quantum simulator itself. This coupling causes hole states created by photon losses to be rapidly refilled, and the system's many-body gap prevents further photons from being added once the strongly correlated ground state is reached. The fractional quantum Hall state (with a small, transient population of quasihole excitations) is thus the most stable state of the system, and all other configurations will relax toward it over time. The physics described here could be implemented in a circuit QED architecture, and the device parameters needed for our scheme to succeed are in reach of current technology. We also propose a simple 6 qubit device, which could easily be built in the near future, that can act as a proof of principle for our scheme.arXiv:1402.6847v2 [cond-mat.mes-hall]
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wavefunctions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wavefunction is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.PACS numbers: 03.75. Lm,67.85.Hj,03.75.Hh, The interplay between periodic potentials and magnetic fields is an important topic [1][2][3][4][5]. In the tight binding limit, the lattice broadens the Landau levels into a series of finite bandwidth "Hofstadter bands" which can be represented as a self-similar fractal. Since the original band-gaps persist, the integer quantum Hall effects are robust against the lattice. The split degeneracy, however, invalidates many of the analytic arguments used to explain the fractional quantum Hall effect [6][7][8][9], and questions remain about the nature of the interacting system. Here, by adding longer range hoppings to a Hubbard model, we produce a Hamiltonian for which several Hofstadter bands coalesce into a single degenerate manifold. Adding local repulsion between the particles, we show that at appropriate filling factors the Laughlin wavefunction becomes an exact ground-state.In a uniform magnetic field, the most general hopping Hamiltonian on a two-dimensional square lattice iswhere the position of the j'th lattice site is written in complex notation as z j = x j + iy j , and z = z k − z j . The operators a j annihilate an atom at site j. The phase factor z j z * − z * j z φ = 2i (x j y − y j x) φ, corresponds to a uniform magnetic field in the symmetric gauge, with flux φ through each plaquette. This flux is only defined modulo 1, and having a full flux quantum through each plaquette is gauge equivalent to no flux. We will explicitly assume 0 ≤ φ ≤ 1, and take φ = p/q to be the ratio of two relatively prime integers. If one chooses W to be −t for nearest neighbors and zero otherwise, one reproduces the Hofstadter spectrum [1]. We show that if instead we chooseG (z) ≡ (−1) x+y+xy , the lowest p Hofstadter bands collapses to a single fully degenerate Landau level. Although we work in the symmetric gauge A = (B/2) (xŷ − yx), converting our results to other gauges is trivial: under a gauge transformation A(r) → A(r) + ∇Λ(r) and c j → c j e iΛ(r j ) . The flux is measured in units of φ 0 = h/e, where h is Planck's constant, and e is the electric charge. Our derivation of this Hamiltonian is similar to one...
Thin streams of liquid commonly break up into characteristic droplet patterns owing to the surface-tension-driven Plateau-Rayleigh instability. Very similar patterns are observed when initially uniform streams of dry granular material break up into clusters of grains, even though flows of macroscopic particles are considered to lack surface tension. Recent studies on freely falling granular streams tracked fluctuations in the stream profile, but the clustering mechanism remained unresolved because the full evolution of the instability could not be observed. Here we demonstrate that the cluster formation is driven by minute, nanoNewton cohesive forces that arise from a combination of van der Waals interactions and capillary bridges between nanometre-scale surface asperities. Our experiments involve high-speed video imaging of the granular stream in the co-moving frame, control over the properties of the grain surfaces and the use of atomic force microscopy to measure grain-grain interactions. The cohesive forces that we measure correspond to an equivalent surface tension five orders of magnitude below that of ordinary liquids. We find that the shapes of these weakly cohesive, non-thermal clusters of macroscopic particles closely resemble droplets resulting from thermally induced rupture of liquid nanojets.
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