Playing relativistic billiards beyond graphene

Sadurní, E.; Seligman, T. H.; Mortessagne, Fabrice

doi:10.1088/1367-2630/12/5/053014

Cited by 50 publications

(67 citation statements)

References 47 publications

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“…Solano and coworkers [21] demonstrated the mapping of the Dirac oscillator onto the Jaynes-Cummings model. Reference [22] reported the realization of a Dirac oscillator in a microwave system, with further proposals involving fiber Bragg gratings [23], hexagonal structures of graphene [24], superconducting qubits [3], and optomechanical arrays [26].…”

Section: N T T B J 1 B P O S H R T O R B M / X 3 R I Z J R U D X a D mentioning

confidence: 99%

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

et al. 2018

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An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.

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Section: N T T B J 1 B P O S H R T O R B M / X 3 R I Z J R U D X a D mentioning

confidence: 99%

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

et al. 2018

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“…This led to the manufacturing of artificial graphene using two-dimensional electron gases, molecular assemblies, ultracold atoms, [78][79][80][81][82] or photonic crystals. [83][84][85][86][87][88][89][90] We exploited this fact to simulate the spectral properties of graphene with microwave resonators that were constructed by squeezing a photonic crystal, which is composed of several hundreds of metallic cylinders arranged on a triangular lattice, between two metal plates. The shape of its band structure, i.e., of its frequencies of wave propagation as function of the two components of the quasimomentum vector, is equivalent to that of the conductance and the valence band in graphene, e.g., for its 1st and its 2nd band.…”

Section: Spectral Properties Of Superconducting Microwave Diracmentioning

confidence: 99%

Quantum and wave dynamical chaos in superconducting microwave billiards

Dietz

Richter

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.

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“…In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30]. Very recently a one dimensional version of the Dirac oscillator has been realised experimentally [31] for the first time with realistic prospects to realise in the near future the two dimensional version of the Dirac oscillator which may be feasible using networks of microwave coaxial cables [32][33][34]. It is interesting to note that a further interaction in the form of a homogeneous magnetic field can still be incorporated in the Dirac oscillator keeping the system still exactly solvable [28,[35][36][37][38] and this combined system has quite interesting properties.…”

Section: Introductionmentioning

confidence: 99%

Re-entrant phase transitions in non-commutative quantum mechanics

Panella

Roy

2016

J. Phys.: Conf. Ser.

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Abstract. We discuss the (2+1)-dimensional Dirac oscillator in a magnetic field in non commutative quantum mechanics. The system is known to be characterised by a left rightchiral phase transition in ordinary Quantum mechanics. We show that the momentum noncommutativity shifts the know phase transition while the space non commutativity introduces a new right-left chiral quantum phase transition giving rise to the intriguing phenomenon of re-entrant phase transition observed in condensed matter as well as in black hole physics. IntroductionOn the basis that both string theory and quantum gravity indicate that space-time can be non-commutative [1-4] several quantum mechanical systems have been studied by a number of authors to determine the role of noncommutativity parameters on a variety of physical observables [5][6][7][8][9][10][11][12][13][14].The Dirac oscillator on the other hand is one of the very few relativistic systems which is exactly solvable [15][16][17][18][19][20][21][22]. In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30]. Very recently a one dimensional version of the Dirac oscillator has been realised experimentally [31] for the first time with realistic prospects to realise in the near future the two dimensional version of the Dirac oscillator which may be feasible using networks of microwave coaxial cables [32][33][34]. It is interesting to note that a further interaction in the form of a homogeneous magnetic field can still be incorporated in the Dirac oscillator keeping the system still exactly solvable [28,[35][36][37][38] and this combined system has quite interesting properties. In some recent papers it has been shown that for this combined system there is a chirality phase transition if the magnitude of the magnetic field either exceeds or is less than a critical value B cr (which also depends on the oscillator strength) [39,40]. A consequence of this chirality phase transition is that the spectrum is different for B > B cr and B < B cr , B being the magnetic field strength.Our objective here is to analyse the same system, a 2D Dirac oscillator within a constant magnetic field, but in the framework of non-commutative space and momentum coordinates. It will be shown that in this case the critical value of the magnetic field depends not only on the oscillator strength but on the non-commutativity parameters as well. The interesting feature which we would like to emphasise, is that beside the two left-and right-chiral phases present also in the commutative case, in the non-commutative scenario there appear also a new third

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Playing relativistic billiards beyond graphene

Cited by 50 publications

References 47 publications

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

Quantum and wave dynamical chaos in superconducting microwave billiards

Re-entrant phase transitions in non-commutative quantum mechanics

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