26 research outputs found
Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice
We consider the Bose-Hubbard model in a two dimensional rotating optical
lattice and investigate the consequences of the effective magnetic field
created by rotation. Using a Gutzwiller type variational wavefunction, we find
an analytical expression for the Mott insulator(MI)-Superfluid(SF) transition
boundary in terms of the maximum eigenvalue of the Hofstadter butterfly. The
dependence of phase boundary on the effective magnetic field is complex,
reflecting the self-similar properties of the single particle energy spectrum.
Finally, we argue that fractional quantum Hall phases exist close to the MI-SF
transition boundaries, including MI states with particle densities greater than
one.Comment: 5 pages,3 figures. High resolution figures available upon reques
P-band in a rotating optical lattice
We investigate the effects of rotation on the excited bands of a tight
binding lattice, focusing particulary on the first excited (p-) band. Both the
on-site energies and the hopping between lattice sites are modified by the
effective magnetic field created by rotation, causing a non-trivial splitting
and magnetic fine structure of the p-band. We show that Peierls substitution
can be modified to describe p-band under rotation, and use this method to
derive an effective Hamiltonian. We compare the spectrum of the effective
Hamiltonian with a first principles calculation of the magnetic band structure
and find excellent agreement, confirming the validity of our approach. We also
discuss the on-site interaction terms for bosons and argue that many-particle
phenomena in a rotating p-band can be investigated starting from this effective
Hamiltonian.Comment: 7 pages, 4 figures, new discussion of effective Hamiltonian,
references adde
Fractional quantum Hall states of photons in an array of dissipative coupled cavities
We report a theoretical study of the collective optical response of a
two-dimensional array of nonlinear cavities in the impenetrable photon regime
under a strong artificial magnetic field. Taking advantage of the
non-equilibrium nature of the photon gas, we propose an experimentally viable
all-optical scheme to generate and detect strongly correlated photon states
which are optical analogs of the Laughlin states of fractional quantum Hall
physics.Comment: 6 pages including the Supplemental Material (accepted for publication
in Phys. Rev. Lett.
Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
We consider a gas of non-interacting spinless fermions in a rotating optical
lattice and calculate the density profile of the gas in an external confinement
potential. The density profile exhibits distinct plateaus, which correspond to
gaps in the single particle spectrum known as the Hofstadter butterfly. The
plateaus result from insulating behavior whenever the Fermi energy lies within
a gap. We discuss the necessary conditions to realize the Hofstadter insulator
in a cold atom setup and show how the quantized Hall conductance can be
measured from density profiles using the St\v{r}eda formula.Comment: 4 pages, 4 figure
Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field
Extensions of Berry's phase and the quantum Hall effect have led to the
discovery of new states of matter with topological properties. Traditionally,
this has been achieved using gauge fields created by magnetic fields or spin
orbit interactions which couple only to charged particles. For neutral
ultracold atoms, synthetic magnetic fields have been created which are strong
enough to realize the Harper-Hofstadter model. Despite many proposals and major
experimental efforts, so far it has not been possible to prepare the ground
state of this system. Here we report the observation of Bose-Einstein
condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum
per lattice unit cell. The diffraction pattern of the superfluid state directly
shows the momentum distribution on the wavefuction, which is gauge-dependent.
It reveals both the reduced symmetry of the vector potential and the twofold
degeneracy of the ground state. We explore an adiabatic many-body state
preparation protocol via the Mott insulating phase and observe the superfluid
ground state in a three-dimensional lattice with strong interactions.Comment: 6 pages, 5 figures. Supplement: 6 pages, 4 figure
Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering
Synthetic magnetism has been used to control charge neutral excitations for
applications ranging from classical beam steering to quantum simulation. In
optomechanics, radiation-pressure-induced parametric coupling between optical
(photon) and mechanical (phonon) excitations may be used to break time-reversal
symmetry, providing the prerequisite for synthetic magnetism. Here we design
and fabricate a silicon optomechanical circuit with both optical and mechanical
connectivity between two optomechanical cavities. Driving the two cavities with
phase-correlated laser light results in a synthetic magnetic flux, which in
combination with dissipative coupling to the mechanical bath, leads to
nonreciprocal transport of photons with 35dB of isolation. Additionally,
optical pumping with blue-detuned light manifests as a particle non-conserving
interaction between photons and phonons, resulting in directional optical
amplification of 12dB in the isolator through direction. These results indicate
the feasibility of utilizing optomechanical circuits to create a more general
class of nonreciprocal optical devices, and further, to enable novel
topological phases for both light and sound on a microchip.Comment: 18 pages, 8 figures, 4 appendice
Out-of-equilibrium physics in driven dissipative coupled resonator arrays
Coupled resonator arrays have been shown to exhibit interesting many- body
physics including Mott and Fractional Hall states of photons. One of the main
differences between these photonic quantum simulators and their cold atoms
coun- terparts is in the dissipative nature of their photonic excitations. The
natural equi- librium state is where there are no photons left in the cavity.
Pumping the system with external drives is therefore necessary to compensate
for the losses and realise non-trivial states. The external driving here can
easily be tuned to be incoherent, coherent or fully quantum, opening the road
for exploration of many body regimes beyond the reach of other approaches. In
this chapter, we review some of the physics arising in driven dissipative
coupled resonator arrays including photon fermionisa- tion, crystallisation, as
well as photonic quantum Hall physics out of equilibrium. We start by briefly
describing possible experimental candidates to realise coupled resonator arrays
along with the two theoretical models that capture their physics, the
Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the
analytical and sophisticated numerical methods required to tackle these systems
is included.Comment: Chapter that appeared in "Quantum Simulations with Photons and
Polaritons: Merging Quantum Optics with Condensed Matter Physics" edited by
D.G.Angelakis, Quantum Science and Technology Series, Springer 201
Topological Photonics
Topology is revolutionizing photonics, bringing with it new theoretical
discoveries and a wealth of potential applications. This field was inspired by
the discovery of topological insulators, in which interfacial electrons
transport without dissipation even in the presence of impurities. Similarly,
new optical mirrors of different wave-vector space topologies have been
constructed to support new states of light propagating at their interfaces.
These novel waveguides allow light to flow around large imperfections without
back-reflection. The present review explains the underlying principles and
highlights the major findings in photonic crystals, coupled resonators,
metamaterials and quasicrystals.Comment: progress and review of an emerging field, 12 pages, 6 figures and 1
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