The electronic circulator, and its close relative the gyrator, are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory, but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative non-reciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an ohmically-contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90 degrees. In this limit we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the a.c. wavelength. An experiment is proposed to achieve GHz-band gyration in millimetre (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realising a Hall gyrator is also analysed.Comment: 18 pages, 15 figures, ~5 MB. V3: sections V-VIII revisited plus other minor changes, Fig 2 added. Submitted to PR
The ν=5/2 anti-Pfaffian state and the ν=2/3 state are believed to have an edge composed of counterpropagating charge and neutral modes. This situation allows the generation of a pure thermal bias between two composite edge states across a quantum point contact as was experimentally established by Bid et al. [Nature 466, 585 (2010)]. We show that replacing the quantum point contact by a quantum dot provides a natural way for detecting the neutral modes via the dc current generated by the thermoelectric response of the dot. We also show that the degeneracies of the dot spectrum, dictated by the conformal field theories describing these states, induce asymmetries in the thermoelectric current peaks. This in turn provides a direct fingerprint of the corresponding conformal field theory.
Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and nonAbelian Read-Rezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, involving charged and neutral parts, and the fusion rules.arXiv:0909.3588v1 [cond-mat.mes-hall]
OverviewThe fractional quantum Hall effect is a collective quantum phenomenon of two-dimensional electrons placed in a strong perpendicular magnetic field (B ∼ 1 − 10 Tesla) and at very low temperature (T ∼ 50 − 500 mK). It manifests itself in the measure of the transverse (σ xy ) and longitudinal (σ xx ) conductances as functions of the magnetic field. The Hall conductance σ xy shows the characteristic step-like behavior: at each step (plateau), it is quantized in rational multiples of the quantum unit of conductance e 2 /h: σ xy = ν e 2 h ; furthermore, at the plateaus centers the longitudinal resistance vanishes. These features are independent on the microscopic details of the samples; in particular, the quantization of σ xy is very accurate, with experimental errors of the order 10 −8 Ω. The rational number ν is the filling fraction of occupied one-particle states at the given value of magnetic field.The fractional Hall effect is characterized by a non-perturbative gap due to the Coulomb interaction among electrons in strong fields. The microscopic theory is impracticable, besides numerical analysis; thus, effective theories, effective field theories in particular, are employed to study these systems. The first step was made by Laughlin, who proposed the trial ground state wave function for fillings ν = , · · · describing the main physical properties of the Hall effect. One general feature is that the electrons form a fluid with gapped excitations in the bulk, the so-called incompressible fluid. In a finite sample, the incompressible fluid gives rise to edge excitations, that are gapless and responsible for the conduction properties. Therefore the low-energy effective field theory should describe these edge degrees of freedom.The Laughlin theory revealed that the excitations are "anyons", i.e. quasiparticles with fractional values of charge and exchange statistics. The latter is a possibility in bidimensional quantum systems, where the statistics of particles is described by the braid group instead of the permutation group of higher-dimensional systems. Each filling fraction corresponds to a different state of matter that is characterized by specific fractional values of charge and statistics. The braiding of quasiparticles can also occur for multiplets of degenerate excitations, by means of multi-dimensional unitary transformations; in this case, called non-Abelian fractional statistics, two different braidings do not commute. The corresponding non-Abelian quasiparticles are degenerate for fixed positions and given quantum numbers.Non-Abelian anyons are candidate for implementing topological quantum computations according to the proposal by Kitaev and others. Since Anyons are non-perturbative collective excitations, they are less affected by decoherence due to local disturbances. III IVExperimental observation of non-Abelian statistics is a present challenge.The topological fluids, such as the quantum Hall fluid can be described by the ChernSimon effective field theory in the low-energy long-range limit. Th...
Using an approach inspired from Spin Glasses, we show that the multimode disordered Dicke model is equivalent to a quantum Hopfield network. We propose variational ground states for the system at zero temperature, which we conjecture to be exact in the thermodynamic limit. These ground states contain the information on the disordered qubit-photon couplings. These results lead to two intriguing physical implications. First, once the qubit-photon couplings can be engineered, it should be possible to build scalable pattern-storing systems whose dynamics is governed by quantum laws. Second, we argue with an example how such Dicke quantum simulators might be used as a solver of "hard" combinatorial optimization problems. PACS numbers:The connection of experimentally realizable quantum systems with computation contains promising perspectives from both the fundamental and the technological viewpoint [1,2]. For example, quantum computational capabilities can be implemented by "quantum gates" [3] and by the so-called "adiabatic quantum optimization" technique [4-6]. Today's experimental technology of highly controllable quantum simulators, recently used for testing theoretical predictions in a wide range of areas of physics [7][8][9], offers new opportunities for exploring computing power for quantum systems.In the case of light-matter interaction at the quantum level, the reference benchmark is the Dicke model [10]. Studies of its equilibrium properties have predicted a superradiant transition to occur in the strong coupling and low temperature regime [11][12][13]. The superradiant phase is characterized by a macroscopic number of atoms in the excited state whose collective behaviour produces an enhancement of spontaneous emission (proportional to the number of cooperating atoms in the sample). Crucially, this phenomenology is in direct link with experimentally feasible quantum simulators. Recently, Nagy and coworkers [14] argued that the Dicke model effectively describes the self-organization phase transition of a BoseEinstein condensate (BEC) in an optical cavity [15,16]. Additionally, Dimer and colleagues [17] proposed a Cavity QED realization of the Dicke model based on cavitymediated Raman transitions, closer in spirit to the original Dicke's idea. Evidence of superradiance in this system is reported in [18]. An implementation of generalized Dicke models in hybrid quantum systems has also been put forward [19]. More generally, Dicke-like Hamiltonians describe a variety of physical systems, ranging from Circuit QED [20][21][22][23][24] to Cavity QED with Dirac fermions in graphene [25][26][27]. Additionally, disorder and frustration of the atom-photon couplings have an important role FIG. 1: In the Dicke model, photons (yellow lines) mediate a long range interaction between qubits (green circles). The drawing sketches schematically a six qubits system within its fully-connected graph and its internal level structure. In the standard single-mode Dicke model the exchange coupling is fixed at the same value for every p...
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