Publisher’s Note: Visual Observation of Zener Tunneling [Phys. Rev. Lett.<b>96</b>, 023901 (2006)]

Trompeter, Henrike; Pertsch, Thomas; Lederer, F.; Michaelis, Dirk; Streppel, Ulrich; Bräuer, Andreas; Peschel, Ulf

doi:10.1103/physrevlett.96.039906

Cited by 83 publications

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“…Examples of previous studies include the use of waveguide arrays [6,7], photonic crystals [8][9][10][11] and meta-materials [12-14] to achieve various beam propagation effects within these structures. Moreover, by introducing inhomogeneity into these structures [15,16], one can realize photon flow that emulates electron motion under electric field [17][18][19].Complementary to these works, which have largely focused on spatial degrees of freedom, our results here show that temporal degrees of freedom in a dynamic structure can also be quite useful in the control of electromagnetic wave propagations in space. Unlike the spatial (i.e.…”

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confidence: 53%

“…Examples of previous studies include the use of waveguide arrays [6,7], photonic crystals [8][9][10][11] and meta-materials [12][13][14] to achieve various beam propagation effects within these structures. Moreover, by introducing inhomogeneity into these structures [15,16], one can realize photon flow that emulates electron motion under electric field [17][18][19].…”

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confidence: 99%

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Controlling the Flow of Light Using the Inhomogeneous Effective Gauge Field that Emerges from Dynamic Modulation

2013

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We show that the effective gauge field for photons provides a versatile platform for controlling the flow of light. As an example we consider a photonic resonator lattice where the coupling strength between nearest neighbor resonators are harmonically modulated. By choosing different spatial distributions of the modulation phases, and hence imposing different inhomogeneous effective magnetic field configurations, we numerically demonstrate a wide variety of propagation effects including negative refraction, one-way mirror, and on and off-axis focusing. Since the effective gauge field is imposed dynamically after a structure is constructed, our work points to the importance of the temporal degree of freedom for controlling the spatial flow of light.It was recently recognized that when a photonic structure undergoes dynamic refractive index modulation, the phase of the modulation creates an effective gauge potential and effective magnetic field for photons [1,3]. The effective magnetic field can induce photonic phenomena similar to charged particles under real magnetic field, such as a photonic one-way edge mode [1] and a photonic de Haas-van Alphen effect [4]. In this paper, we further show that the use of inhomogeneous effective gauge fields provide additional degrees of freedom in controlling the flow of light. As examples, we show that one can achieve negative refraction, one-way mirrors, circulators, and focusing, based on the same resonator lattice structure subject to different configurations of inhomogeneous effective gauge fields.Tailoring the propagation of light has been a central goal of nano-photonic research, which is critical for applications in on-chip communications and information processing [5]. Examples of previous studies include the use of waveguide arrays [6,7], photonic crystals [8][9][10][11] and meta-materials [12-14] to achieve various beam propagation effects within these structures. Moreover, by introducing inhomogeneity into these structures [15,16], one can realize photon flow that emulates electron motion under electric field [17][18][19].Complementary to these works, which have largely focused on spatial degrees of freedom, our results here show that temporal degrees of freedom in a dynamic structure can also be quite useful in the control of electromagnetic wave propagations in space. Unlike the spatial (i.e. the structural) degrees of freedom, which are mostly defined by fabrication processes, the modulation phases can be readily changed in the dynamic structure, after the structure is constructed. Moreover, non-reciprocity, or timereversal symmetry breaking, which is difficult to achieve * Current address: Thomas J. Watson, Sr

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confidence: 53%

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confidence: 99%

Controlling the Flow of Light Using the Inhomogeneous Effective Gauge Field that Emerges from Dynamic Modulation

2013

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“…Besides solid state physics, where the phenomenon has been observed only in recent times after the development of the superlattice technology [2], it is now possible to observe BO also in other fields such as nonlinear optics, using light beams in arrays of waveguides [3] or in photorefractive crystals [4], and atomic physics, using Bose-Einstein condensates (BEC) loaded in optical lattices (OLs) [5,6,7]. Apart its fundamental significance, the interest in BO arises mainly from perspectives of their practical applications.…”

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confidence: 99%

Long-Living Bloch Oscillations of Matter Waves in Periodic Potentials

2008

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It is shown that by properly designing the spatial dependence of the nonlinearity it is possible to induce long-living Bloch oscillations of a localized wavepacket in a periodic potential. The results are supported both by analytical and numerical investigations and are interpreted in terms of matter wave dynamics displaying dozens of oscillation periods without any visible distortion of the wave packet.PACS numbers: 03.75Kk, 03.75Lm, 67.85.HjThe phenomenon of Bloch oscillations (BO), predicted by Bloch in 1928 in his celebrated paper on the dynamics of a band electron in a steady electrical field [1], represents a problem of non exhausted interest. Besides solid state physics, where the phenomenon has been observed only in recent times after the development of the superlattice technology [2], it is now possible to observe BO also in other fields such as nonlinear optics, using light beams in arrays of waveguides [3] or in photorefractive crystals [4], and atomic physics, using Bose-Einstein condensates (BEC) loaded in optical lattices (OLs) [5,6,7]. Apart its fundamental significance, the interest in BO arises mainly from perspectives of their practical applications. In this context we mention the use of BO for metrological tasks, including relatively precise definition of h/m [8] and measurement of forces at the micrometer scale like the Casimir-Polder force [9] and the gravity [10]. Recently, BO were also suggested as a tool for controlling light in coupled-resonator optical waveguides [11]. In these physical contexts BO have been observed mainly in the linear (as first proposed by Bloch) or quasi linear regimes (where the nonlinearity introduces quantitative but not yet qualitative changes). The present experimental settings (both in nonlinear optics and in BECs), however, allow for attaining essentially nonlinear regimes quite easily, this actually being a desirable condition for applications involving localized states.The fact that BO can exist in presence of interactions (nonlinearity) was first recognized in the context of nonlinear discrete systems [12]. For periodic continuous models of the nonlinear Schrödinger (NLS) type, such as ones describing matter waves in OLs, the existence of BO becomes more problematic because of nonlinearity induced instabilities in the underlying linear system. These instabilities can be simply understood by observing that in a usual OL at the edges of an allowed band the effective mass has always opposite signs. This implies that if a Bloch state is modulationally stable (in presence of a constant nonlinearity) at one edge of the band, it must be necessarily unstable at the other band edge [13]. Nonlinearity induced instabilities have been extensively investigated both theoretically [13,14] and experimentally [15]) and have been identified as primary cause for the short life-times of BO of matter waves (the oscillation survives only a few cycles) observed both in numerical [16] and in real experiments [15].In this Letter we show that by properly controlling the instabiliti...

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“…The related high-field phenomenon, Landau-Zener tunneling (LZT) between neighboring bands across the band gap [15,16], was also observed in SSLs for electrons [17,18], and in optical lattices for ultracold atoms [19] and Bose-Einstein condensates [20]. Optical BOs and LZT of light waves have also been observed in time-resolved experiments [21][22][23].…”

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confidence: 92%

Surface Acoustic Bloch Oscillations, the Wannier-Stark Ladder, and Landau-Zener Tunneling in a Solid

et al. 2010

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We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and LandauZener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The use of a planar geometry for the realization of the Bloch oscillations and Landau-Zener tunneling allows a direct access to the elastic field distribution. The vertical surface displacement has been measured by interferometry. DOI: 10.1103/PhysRevLett.104.165502 PACS numbers: 63.20.Àe, 43.35.+d, 63.22.Àm, 68.35.Àp Bloch oscillations (BOs) of an electron in a periodic potential under a constant electric field is a paradigm quantum effect [1,2]. BOs of the wave-packet group velocity are the result of the interplay between the particlelike acceleration by a constant driving force and wave Bragg reflection in the periodic potential. The frequencydomain counterpart of BOs is the equidistant WannierStark ladder (WSL) of localized states in a perturbed periodic system [3]. Electron BOs and WSL have been demonstrated in a number of experiments after the advent of semiconductor superlattices (SSLs) [4]. The WSL leads to resonances of the density of electronic states which were observed for the first time in optical spectra in SSLs [5]. BOs were first observed in time-resolved optical experiments in biased SSLs as oscillations of electron wave packets [6][7][8][9][10], and later as a periodic motion of ensembles of ultracold atoms [11,12] and Bose-Einstein condensates [13,14] in optical lattices. The related high-field phenomenon, Landau-Zener tunneling (LZT) between neighboring bands across the band gap [15,16], was also observed in SSLs for electrons [17,18] In this Letter, we demonstrate that fundamental effects of quantum-wave transport in a perturbed periodic potential such as BOs, WSL, and LZT can be studied with surface acoustic waves (SAWs) in a solid. Our experimental results, including multiple LZ-like transitions between the anticrossed surface acoustic WS states, are described by a theoretical model developed by us. The used planar geometry allows the direct access to the elastic field distribution of the corresponding WS and LZ eigenstates.In our approach, we employ SAW cavities separated by acoustic Bragg reflectors (BRs). These structures are defined by locally changing the SAW propagation properties via the deposition of thin gold stripes in-between a LiNbO 3 SAW delay line (see Fig. 1). The BRs are efficient barriers, presenting high reflectivity for an incoming wave packet. This arises from the destructive interference of the properly arranged set of reflectors that creates a stop-band in the transmission spectrum for the incoming wave. Further-

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Publisher’s Note: Visual Observation of Zener Tunneling [Phys. Rev. Lett.96, 023901 (2006)]

Cited by 83 publications

References 0 publications

Controlling the Flow of Light Using the Inhomogeneous Effective Gauge Field that Emerges from Dynamic Modulation

Controlling the Flow of Light Using the Inhomogeneous Effective Gauge Field that Emerges from Dynamic Modulation

Long-Living Bloch Oscillations of Matter Waves in Periodic Potentials

Surface Acoustic Bloch Oscillations, the Wannier-Stark Ladder, and Landau-Zener Tunneling in a Solid

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