Photon Propagation in a Discrete Fiber Network: An Interplay of Coherence and Losses

Regensburger, Alois; Bersch, Christoph; Hinrichs, Benjamin; Onishchukov, G.; Schreiber, Andreas; Silberhorn, Christine; Peschel, Ulf

doi:10.1103/physrevlett.107.233902

Cited by 157 publications

(171 citation statements)

References 32 publications

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“…By switching off one of the two loops in a cyclic fashion after every second time step m, the system is converted into a lossy mesh lattice as discussed in ref. 37. The resulting propagation is given by a diffusion equation leading to a coherent splitting of the initial pulse into a chain of pulses with a Gaussian envelope.…”

Section: Methodsmentioning

confidence: 99%

Experimental measurement of the Berry curvature from anomalous transport

et al. 2017

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The geometric properties of energy bands underlie fascinating phenomena in many systems, including solid-state, ultracold gases and photonics. The local geometric characteristics such as the Berry curvature 1 can be related to global topological invariants such as those classifying the quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a coherent wavepacket. Here, we experimentally demonstrate that the wavepacket dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time evolution of a wavepacket in a one-dimensional geometric 'charge' pump, where the Berry curvature leads to an anomalous displacement of the wavepacket. This is both the first direct observation of Berry curvature e ects in an optical system, and a proof-ofprinciple demonstration that wavepacket dynamics can serve as a high-resolution tool for mapping out geometric properties.The Berry curvature is a geometrical property of an energy band, which plays a key role in many physical phenomena as it encodes how eigenstates evolve as a local function of parameters 1 . In a twodimensional (2D) quantum Hall system, for example, the integral of the Berry curvature over the 2D Brillouin zone determines the Chern number: a global topological invariant that underlies the quantization of Hall transport for a 2D filled energy band 2 . As first explained by Thouless 3 , there can be an analogous topological quantization of particle transport in a 1D band insulator, when the lattice potential is 'pumped' , that is, is slowly and periodically modulated in time. Also in this case, the geometrical and topological properties are defined for an effective 2D parameter space, but now one spanned by the 1D Bloch momentum and the external periodic pumping parameter.A local non-zero Berry curvature can have striking physical effects in both 2D systems and 1D pumps, regardless of whether the global topological Chern number is non-trivial. In the simplest case, a semi-classical wavepacket moves as a coherent object governed by classical equations of motion with an additional 'anomalous' Hall velocity due to the geometrical Berry curvature at its centre-ofmass, as an external force is applied or as the control parameter is pumped 1,4 . As highlighted further below, this anomalous transport can be understood physically as the Berry curvature acting like a magnetic field in parameter space [5][6][7] .In recent years, there have been many landmark experiments to engineer and study geometrical and topological energy bands in ultracold gases and photonics . In photonics, for example, topological edge states have been studied in a wide variety of (effectively) 1D set-ups, such as quantum walks 14 and pumping in optical quasicrystals 13,29,30 , as well as in 2D quantum Hall-like systems of photonic crystals 9-11 , propagating waveguides 12 and silico...

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Section: Methodsmentioning

confidence: 99%

Experimental measurement of the Berry curvature from anomalous transport

et al. 2017

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“…Such configurations have been systematically employed to investigate a number of issues ranging from discrete quantum walks [44][45][46][47] to Bloch oscillations and fractal patterns [43,48]. While spatial realizations of such mesh lattices have also been reported [47,49], time-multiplexed fiber loop schemes have so far demonstrated a high degree of flexibility [43,45].…”

Section: Optical Mesh Lattices In the Time Domainmentioning

confidence: 99%

“…Lately, the temporal equivalent of an optical mesh lattice has been experimentally realized using timemultiplexed loop arrangements [43]. Such configurations have been systematically employed to investigate a number of issues ranging from discrete quantum walks [44][45][46][47] to Bloch oscillations and fractal patterns [43,48].…”

Section: Optical Mesh Lattices In the Time Domainmentioning

confidence: 99%

Optical mesh lattices withPTsymmetry

Miri

Regensburger

Peschel³

et al. 2012

Phys. Rev. A

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111

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We investigate a new class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions. These networks are composed of waveguide arrays that are discretely coupled while phase elements are also inserted to discretely control their effective potentials and can be realized both in the temporal and the spatial domain. Their band structure and impulse response is studied in both the passive and parity-time (PT ) symmetric regime. The possibility of band merging and the emergence of exceptional points along with the associated optical dynamics are considered in detail both above and below the PT -symmetry breaking point. Finally unidirectional invisibility in PT -synthetic mesh lattices is also examined along with possible superluminal light transport dynamics.

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“…This approach was first formulated for frequency-encoded quantum walks [33]. From an experimental perspective, a further key advance was the development of optical cavities that implement time-encoded walks [29,30]. In this case, the walker's location is represented by the time at which a pulse completes a round trip of a cavity [29,30].…”

mentioning

confidence: 99%

Large scale quantum walks by means of optical fiber cavities

Boutari

Feizpour

Barz

et al. 2016

J. Opt.

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We demonstrate a platform for implementing quantum walks that overcomes many of the barriers associated with photonic implementations. We use coupled fiber-optic cavities to implement time-bin encoded walks in an integrated system. We show that this platform can achieve very low losses combined with high-fidelity operation, enabling an unprecedented large number of steps in a passive system, as required for scenarios with multiple walkers. Furthermore the platform is reconfigurable, enabling variation of the coin, and readily extends to multidimensional lattices. We demonstrate variation of the coin bias experimentally for three different values. INTRODUCTIONQuantum walks are the quantum counterparts to random walks. A quantum walker moves by superpositions of possible paths, resulting in a probability amplitude for being observed at a particular position [1][2][3]. Optical multiport interferometers provide an attractive implementation for quantum walks, since optical fields naturally exhibit coherence between pathways and allow multi-walker scenarios using multiple single photons. However, this approach is susceptible to losses, which limit the achievable scale before being overtaken by noise, and which abrogate many of the advantages implied for applications in quantum information processing [4][5][6][7][8][9][10][11][12]. This challenge motivates the development of low-loss, modular, guided-wave interferometer networks for quantum walks.Quantum walks with multiple interacting walkers have been shown to realize universal quantum computation [13]. For the case of multiple non-interacting walkers, quantum walks are also thought to have quantum computational power, as shown by the boson sampling problem [14]. Quantum walks with a single walker can implement quantum computation, though this requires an exponentially large graph [15,16]. A key feature of quantum walks as information processors is that they do not require time-dependent feedforward control. Quantum walks, both discrete and continuous, have been realised using cold atoms [17,18], single optically trapped atoms [19], trapped ions [20][21][22], and photons. Optical systems have been used to implement quantum walks using bulk optics [23,24], photonic chips [25][26][27][28], fiber optics [29], and hybrid bulkfiber optic approaches [30][31][32].In most experimental implementations, the quantum walk takes place over spatial locations arranged in a lattice. The physical size of the lattice then determines the maximum size of the walk. This limitation can be avoided by use of optical cavities, in which case the number of physical elements required is independent of the size of the walk. This approach was first formulated for frequency-encoded quantum walks [33]. From an experimental perspective, a further key advance was the development of optical cavities that implement time-encoded walks [29,30]. In this case, the walker's location is represented by the time at which a pulse completes a round trip of a cavity [29,30]. In practice, the achievable scale of t...

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Photon Propagation in a Discrete Fiber Network: An Interplay of Coherence and Losses

Cited by 157 publications

References 32 publications

Experimental measurement of the Berry curvature from anomalous transport

Experimental measurement of the Berry curvature from anomalous transport

Optical mesh lattices withPTsymmetry

Large scale quantum walks by means of optical fiber cavities

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