82 research outputs found
Majorana-Like Modes of Light in a One-Dimensional Array of Nonlinear Cavities
The search for Majorana fermions in p-wave paired fermionic systems has
recently moved to the forefront of condensed-matter research. Here we propose
an alternative route and show theoretically that Majorana-like modes can be
realized and probed in a driven-dissipative system of strongly correlated
photons consisting of a chain of tunnel-coupled cavities, where p-wave pairing
effectively arises from the interplay between strong on-site interactions and
two-photon parametric driving. The nonlocal nature of these exotic modes could
be demonstrated through cross-correlation measurements carried out at the ends
of the chain---revealing a strong photon bunching signature---and their
non-Abelian properties could be simulated through tunnel-braid operations.Comment: 5 pages, 2 figures; with Supplemental Material (12 pages
Seeing bulk topological properties of band insulators in small photonic lattices
We present a general scheme for measuring the bulk properties of
non-interacting tight-binding models realized in arrays of coupled photonic
cavities. Specifically, we propose to implement a single unit cell of the
targeted model with tunable twisted boundary conditions in order to simulate
large systems and, most importantly, to access bulk topological properties
experimentally. We illustrate our method by demonstrating how to measure
topological invariants in a two-dimensional quantum Hall-like model.Comment: 5 pages, 2 figures; with Supplemental Material (2 pages
Device independent state estimation based on Bell's inequalities
The only information available about an alleged source of entangled quantum
states is the amount by which the Clauser-Horne-Shimony-Holt (CHSH)
inequality is violated: nothing is known about the nature of the system or the
measurements that are performed. We discuss how the quality of the source can
be assessed in this black-box scenario, as compared to an ideal source that
would produce maximally entangled states (more precisely, any state for which
). To this end, we introduce several inequivalent notions of
fidelity, each one related to the use one can make of the source after having
assessed it; and we derive quantitative bounds for each of them in terms of the
violation . We also derive a lower bound on the entanglement of the source
as a function of only.Comment: 8 pages, 2 figures. Added appendices containing proof
Topology by dissipation
Topological states of fermionic matter can be induced by means of a suitably
engineered dissipative dynamics. Dissipation then does not occur as a
perturbation, but rather as the main resource for many-body dynamics, providing
a targeted cooling into a topological phase starting from an arbitrary initial
state. We explore the concept of topological order in this setting, developing
and applying a general theoretical framework based on the system density matrix
which replaces the wave function appropriate for the discussion of Hamiltonian
ground-state physics. We identify key analogies and differences to the more
conventional Hamiltonian scenario. Differences mainly arise from the fact that
the properties of the spectrum and of the state of the system are not as
tightly related as in a Hamiltonian context. We provide a symmetry-based
topological classification of bulk steady states and identify the classes that
are achievable by means of quasi-local dissipative processes driving into
superfluid paired states. We also explore the fate of the bulk-edge
correspondence in the dissipative setting, and demonstrate the emergence of
Majorana edge modes. We illustrate our findings in one- and two-dimensional
models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure
Efficient algorithm to compute the Berry conductivity
We propose and construct a numerical algorithm to calculate the Berry conductivityin topological band insulators. The method is applicable to cold atomsystems as well as solid state setups, both for the insulating case where the Fermienergy lies in the gap between two bulk bands as well as in the metallic regime.This method interpolates smoothly between both regimes. The algorithm isgauge-invariant by construction, efficient, and yields the Berry conductivity withknown and controllable statistical error bars. We apply the algorithm to severalparadigmatic models in the field of topological insulators, including Haldaneʼsmodel on the honeycomb lattice, the multi-band Hofstadter model, and the BHZmodel, which describes the 2D spin Hall effect observed in CdTe/HgTe/CdTequantum well heterostructures
Quantum networks reveal quantum nonlocality
The results of local measurements on some composite quantum systems cannot be
reproduced classically. This impossibility, known as quantum nonlocality,
represents a milestone in the foundations of quantum theory. Quantum
nonlocality is also a valuable resource for information processing tasks, e.g.
quantum communication, quantum key distribution, quantum state estimation, or
randomness extraction. Still, deciding if a quantum state is nonlocal remains a
challenging problem. Here we introduce a novel approach to this question: we
study the nonlocal properties of quantum states when distributed and measured
in networks. Using our framework, we show how any one-way entanglement
distillable state leads to nonlocal correlations. Then, we prove that
nonlocality is a non-additive resource, which can be activated. There exist
states, local at the single-copy level, that become nonlocal when taking
several copies of it. Our results imply that the nonlocality of quantum states
strongly depends on the measurement context.Comment: 4 + 3 pages, 4 figure
Realistic loophole-free Bell test with atom-photon entanglement
The establishment of nonlocal correlations, obtained through the violation of
a Bell inequality, is not only important from a fundamental point of view, but
constitutes the basis for device-independent quantum information technologies.
Although several nonlocality tests have been performed so far, all of them
suffered from either the locality or the detection loopholes. Recent studies
have suggested that the use of atom-photon entanglement can lead to Bell
inequality violations with moderate transmission and detection efficiencies. In
this paper we propose an experimental setup realizing a simple atom-photon
entangled state that, under realistic experimental parameters available to
date, achieves a significant violation of the Clauser-Horn-Shimony-Holt
inequality. Most importantly, the violation remains when considering typical
detection efficiencies and losses due to required propagation distances.Comment: 21 pages, 5 figures, 3 table, to appear in Nature Com
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
Experimental estimation of the dimension of classical and quantum systems
An overwhelming majority of experiments in classical and quantum physics make
a priori assumptions about the dimension of the system under consideration.
However, would it be possible to assess the dimension of a completely unknown
system only from the results of measurements performed on it, without any extra
assumption? The concept of a dimension witness answers this question, as it
allows one to bound the dimension of an unknown classical or quantum system in
a device-independent manner, that is, only from the statistics of measurements
performed on it. Here, we report on the experimental demonstration of dimension
witnesses in a prepare and measure scenario. We use pairs of photons entangled
in both polarization and orbital angular momentum to generate ensembles of
classical and quantum states of dimensions up to 4. We then use a dimension
witness to certify their dimensionality as well as their quantum nature. Our
results open new avenues for the device-independent estimation of unknown
quantum systems and for applications in quantum information science.Comment: See also similar, independent and jointly submitted work of J. Ahrens
et al., quant-ph/1111.127
Subwavelength vacuum lattices and atom–atom interactions in two-dimensional photonic crystals
Quantum simulation with cold atoms in optical lattices is an attractive avenue for explorations of quantum many-body physics. A principal challenge in the field is to increase the energy and length scales in current set-ups, thereby reducing temperature and coherence-time requirements. Here, we present a new paradigm for high-density, two-dimensional optical lattices in photonic crystal waveguides. Specially engineered two-dimensional photonic crystals provide a practical platform to trap atoms and engineer their interactions in ways that surpass the limitations of current technologies and enable investigations of novel quantum many-body matter. Our schemes remove the constraint on the lattice constant set by the free-space optical wavelength in favour of deeply sub-wavelength atomic arrays. We further describe possibilities for atom–atom interactions mediated by photons in two-dimensional photonic crystal waveguides with energy scales several orders of magnitude larger than for exchange interactions in free-space lattices and with the capability to engineer strongly long-range interactions
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