arXiv subjects

Avik Dutt

Publications and source records attributed to Avik Dutt.

At least 37 records · Page 2Linked to original sources

arXiv2023

Two-Dimensional Nonlinear Mixing Between a Dissipative Kerr Soliton and Continuous Waves for a Higher-Dimension Frequency Comb

Dissipative Kerr solitons (DKSs) intrinsically exhibit two degrees of freedom through their group and phase rotation velocity. Periodic extraction of the DKS into a waveguide produces a pulse train and yields the resulting optical frequency comb's repetition rate and carrier-envelope offset, respectively. Here, we demonstrate that it is possible to create a system with a single repetition rate but two different phase velocities by employing dual driving forces. By recasting these phase velocities into frequencies, we demonstrate, experimentally and theoretically, that they can mix and create new phase-velocity light following any four-wave mixing process, including both degenerately pumped and non-degenerately pumped effects. In particular, we show that a multiple-pumped DKS may generate a two-dimensional frequency comb, where cascaded nonlinear mixing occurs in the phase velocity dimension as well as the conventional mode number dimension, and where the repetition rate in each dimension differs by orders of magnitude.

physics.optics↗

arXiv2022

Programmable photonic system for quantum simulation in arbitrary topologies

Synthetic dimensions have generated great interest for studying many types of topological, quantum, and many-body physics, and they offer a flexible platform for simulation of interesting physical systems, especially in high dimensions. In this Letter, we describe a programmable photonic device capable of emulating the dynamics of a broad class of Hamiltonians in lattices with arbitrary topologies and dimensions. We derive a correspondence between the physics of the device and the Hamiltonians of interest, and we simulate the physics of the device to observe a wide variety of physical phenomena, including chiral states in a Hall ladder, effective gauge potentials, and oscillations in high-dimensional lattices. Our proposed device opens new possibilities for studying topological and many-body physics in near-term experimental platforms.

quant-ph↗

arXiv2022

Synthetic Frequency Lattices from an Integrated Dispersive Multi-Color Soliton

Dissipative Kerr solitons (DKSs) in optical microresonators have been intensely studied from the perspective of both fundamental nonlinear physics and portable and low power technological applications in communications, sensing, and metrology. In parallel, synthetic dimensions offer the promise of studying physical phenomena with a dimensionality beyond that imposed by geometry, and have been implemented in optics. The interplay of DKS physics with synthetic dimensions promises to unveil numerous new physical and technological insights, yet many fundamental challenges remain. In particular, DKSs intrinsically rely on dispersion to exist while the creation of synthetic frequency lattices typically needs a dispersion-less system. We present a change of paradigm with the creation of a synthetic frequency lattice in the eigenfrequency space of a dispersive multi-color soliton through all-optical nonlinear coupling -- compatible with octave spanning microcombs -- harnessing the interplay between the cavity dispersion and the dispersion-less nature of the DKS. We examine theoretically and experimentally the nonlinear coupling mechanism in a 1~THz repetition rate resonator and demonstrate four-wave mixing Bragg scattering between the different wavepackets forming the multi-color soliton, with the microcomb ranging over 150~THz, yielding a complex all-optical and integrated synthetic frequency lattice.

physics.optics↗

arXiv2022

Time reflection and refraction in synthetic frequency dimension

The duality of space and time in Maxwell's equations has prompted interest in time boundaries and the accompanying temporal analog of spatial reflection and refraction. However, achieving observable time boundary effects at optical frequencies in real materials is challenging. In this work, we demonstrate that time reflection and refraction can be observed in a two-band model centered around a non-zero reference energy. Our model can be physically implemented in the synthetic frequency dimension as a system of two coupled dynamically-modulated ring resonators. We find that modulation at microwave frequencies is sufficient to observe time boundary effects for optical waves in synthetic frequency dimension. Our work shows that implementing multi-band models in synthetic dimensions opens a new avenue for further exploration of time boundaries.

physics.optics↗

arXiv2022

Topological Temporally Mode-Locked Laser

Mode-locked lasers play a key role in modern science and technology. Not only do they lay the foundation for ultrafast optics and play a central role in nonlinear optics, but also they have important applications in imaging, telecommunications, sensing, and computing. While substantial efforts have focused on mode-locking the spectral modes of lasers, relatively little attention has been paid to mode-locking their temporal modes. However, temporal mode-locking presents ample opportunities to develop new technologies and to study the intersection of nonlinear, non-Hermitian, and topological phenomena, which, in recent years, has been a priority for the field of topological physics. Here, we theoretically predict and experimentally realize topological temporal mode-locking in a laser cavity with time-delayed intracavity couplings. These couplings introduce non-Hermitian point-gap topology into the temporal modes of our laser and conspire with an effective nonlocal nonlinearity to generate mode-locked temporal structures in our laser cavity, whose form can be tailored by suitably engineering the underlying couplings. We harness this approach to realize a nonlinearity-driven non-Hermitian skin effect, and we show that the topological temporal modes of our laser are robust against disorder-induced localization. The flexibility and programmability of our topological temporal mode-locking scheme reveals new opportunities to study nonlinear and non-Hermitian topological phenomena in mode-locked photonic resonators and could enable new applications of mode-locked lasers to sensing and optical computing.

physics.optics↗

arXiv2022

Creating boundaries along a synthetic frequency dimension

Synthetic dimensions have garnered widespread interest for implementing high dimensional classical and quantum dynamics on lower dimensional geometries. Synthetic frequency dimensions, in particular, have been used to experimentally realize a plethora of bulk physics effects, such as effective gauge potentials, nontrivial Hermitian as well as non-Hermitian topology, spin-momentum locking, complex long-range coupling, unidirectional frequency conversion, and four-dimensional lattices. However, in synthetic frequency dimensions there has not been any demonstration of boundary effects which are of paramount importance in topological physics due to the bulk edge correspondence, since systems exhibiting synthetic frequency dimensions do not support well-defined sharp boundaries. Here we theoretically elucidate a method to construct boundaries in the synthetic frequency dimension of dynamically modulated ring resonators by strongly coupling it to an auxiliary ring, and provide an experimental demonstration of this method. We experimentally explore various physics effects associated with the creation of such boundaries in the synthetic frequency dimension, including confinement of the spectrum of light, the discretization of the band structure, and the interaction of such boundaries with the topologically protected one-way chiral modes in a quantum Hall ladder. The incorporation of boundaries allows us to observe topologically robust transport of light along the frequency axis, which shows that the frequency of light can be controlled through topological concepts. Our demonstration of such sharp boundaries fundamentally expands the capability of exploring topological physics, and is also of importance for other applications such as classical and quantum information processing in synthetic frequency dimensions.

quant-ph↗

arXiv2022

Roadmap on Topological Photonics

Topological photonics seeks to control the behaviour of the light through the design of protected topological modes in photonic structures. While this approach originated from studying the behaviour of electrons in solid-state materials, it has since blossomed into a field that is at the very forefront of the search for new topological types of matter. This can have real implications for future technologies by harnessing the robustness of topological photonics for applications in photonics devices. This Roadmap surveys some of the main emerging areas of research within topological photonics, with a special attention to questions in fundamental science, which photonics is in an ideal position to address. Each section provides an overview of the current and future challenges within a part of the field, highlighting the most exciting opportunities for future research and developments.

physics.optics↗

arXiv2021

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. In one dimension, it was recently noted theoretically and demonstrated experimentally that the eigenvalue topology is classified by the braid group. The classification of eigenvalue topology in higher dimensions, however, remained an open question. Here, we give a complete description of eigenvalue topology in two and three dimensional systems, including the gapped and gapless cases. We reduce the topological classification problem to a purely computational problem in algebraic topology. In two dimensions, the Brillouin zone torus is punctured by exceptional points, and each nontrivial loop in the punctured torus acquires a braid group invariant. These braids satisfy the constraint that the composite of the braids around the exceptional points is equal to the commutator of the braids on the fundamental cycles of the torus. In three dimensions, there are exceptional knots and links, and the classification depends on how they are embedded in the Brillouin zone three-torus. When the exceptional link is contained in a contractible ball, the classification can be expressed in terms of the knot group of the link. Our results provide a comprehensive understanding of non-Hermitian eigenvalue topology in higher dimensional systems, and should be important for the further explorations of topologically robust open quantum and classical systems.

physics.optics↗

arXiv2021

Smooth double barriers in quantum mechanics

Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle energy, and their dependence on the barrier parameters are obtained for various cases. We also discuss the tunneling time, for which we obtain generalizations of the known results for rectangular barriers.

quant-ph↗

arXiv2021

Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals

We show that two-dimensional non-Hermitian photonic crystals made of lossy material can exhibit non-trivial point gap topology in terms of topological winding in its complex frequency band structure. Such crystals can be either made of lossy isotropic media which is reciprocal, or lossy magneto-optical media which is non-reciprocal. We discuss the effects of reciprocity on the properties of the point gap topology. We also show that such a non-trivial point gap topology leads to non-Hermitian skin effect when the photonic crystal is truncated. In contrast to most previous studies on point gap topology which used tight-binding models, our work indicates that such non-Hermitian topology can studied in photonic crystals, which represent a more realistic system that has technological significance.

cond-mat.mes-hall↗

arXiv2021

Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators

The concept of synthetic dimensions in photonics has attracted rapidly growing interest in the past few years. Among a variety of photonic systems, the ring resonator system under dynamic modulation has been investigated in depth both in theory and experiment, and has proven to be a powerful way to build synthetic frequency dimensions. In this tutorial, we start with a pedagogical introduction to the theoretical approaches in describing the dynamically modulated ring resonator system, and then review experimental methods in building such a system. Moreover, we discuss important physical phenomena in synthetic dimensions, including nontrivial topological physics. Our tutorial provides a pathway towards studying the dynamically modulated ring resonator system, understanding synthetic dimensions in photonics, and discusses future prospects for both fundamental research and practical applications using synthetic dimensions.

physics.optics↗

arXiv2021

Topological Dissipation in a Time-Multiplexed Photonic Resonator Network

Topological phases feature robust edge states that are protected against the effects of defects and disorder. The robustness of these states presents opportunities to design technologies that are tolerant to fabrication errors and resilient to environmental fluctuations. While most topological phases rely on conservative, or Hermitian, couplings, recent theoretical efforts have combined conservative and dissipative couplings to propose new topological phases for ultracold atoms and for photonics. However, the topological phases that arise due to purely dissipative couplings remain largely unexplored. Here we realize dissipatively coupled versions of two prominent topological models, the Su-Schrieffer-Heeger (SSH) model and the Harper-Hofstadter (HH) model, in the synthetic dimensions of a time-multiplexed photonic resonator network. We observe the topological edge state of the SSH and HH models, measure the SSH model's band structure, and induce a topological phase transition between the SSH model's trivial and topological phases. In stark contrast with conservatively coupled topological phases, the topological phases of our network arise from bands of dissipation rates that possess nontrivial topological invariants, and the edge states of these topological phases exhibit isolated dissipation rates that occur in the gaps between the bulk dissipation bands. Our results showcase the ability of dissipative couplings to enable time-reversal symmetry broken topological phases with nonzero Chern numbers, which have proven challenging to realize in the optical domain. Moreover, our time-multiplexed network, with its ability to implement multiple synthetic dimensions, dynamic and inhomogeneous couplings, and time-reversal symmetry breaking synthetic gauge fields, offers a flexible and scalable architecture for future work in synthetic dimensions.

physics.optics↗

arXiv2021

Observation of arbitrary topological windings of a non-Hermitian band

The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian systems, is the non-trivial winding of the energy band in the complex energy plane. Here we provide direct experimental demonstrations of such non-trivial winding, by implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed in a ring resonator undergoing simultaneous phase and amplitude modulations, and by directly characterizing the complex band structures. Moreover, we show that the topological winding can be straightforwardly controlled by changing the modulation waveform. Our results open a pathway for the experimental synthesis and characterization of topologically non-trivial phases in non-conservative systems.

physics.optics↗

arXiv2021

Deterministic photonic quantum computation in a synthetic time dimension

Photonics offers unique advantages as a substrate for quantum information processing, but imposes fundamental scalability challenges. Nondeterministic schemes impose massive resource overheads, while deterministic schemes require prohibitively many identical quantum emitters to realize sizeable quantum circuits. Here we propose a scalable architecture for a photonic quantum computer which needs minimal quantum resources to implement any quantum circuit: a single coherently controlled atom. Optical switches endow a photonic quantum state with a synthetic time dimension by modulating photon-atom couplings. Quantum operations applied to the atomic qubit can be teleported onto the photonic qubits via projective measurement, and arbitrary quantum circuits can be compiled into a sequence of these teleported operators. This design negates the need for many identical quantum emitters to be integrated into a photonic circuit and allows effective all-to-all connectivity between photonic qubits. The proposed device has a machine size which is independent of quantum circuit depth, does not require single-photon detectors, operates deterministically, and is robust to experimental imperfections.

quant-ph↗

arXiv2020

Integrated Nonreciprocal Photonic Devices with Dynamic Modulation

Nonreciprocal components, such as isolators and circulators, are crucial components for photonic systems. In this article we review theoretical and experimental progress towards developing nonreciprocal photonic devices based on dynamic modulation. In particular, we focus on approaches that operate at optical wavelengths and device architectures that have the potential for chip-scale integration. We first discuss the requirements for constructing an isolator or circulator using dynamic modulation. We review a number of different isolator and circulator architectures, including waveguide and resonant devices, and describe their underlying operating principles. We then compare these device architectures from a system-level performance perspective, considering how their figures of merit, such as footprint, bandwidth, isolation, and insertion loss scale with respect to device parameters.

physics.optics↗

arXiv2020

Non-Dissipative Non-Hermitian Dynamics and Exceptional Points in Coupled Optical Parametric Oscillators

Engineered non-Hermitian systems featuring exceptional points can lead to a host of extraordinary phenomena in diverse fields ranging from photonics, acoustics, opto-mechanics, electronics, to atomic physics. Here we introduce and present non-Hermitian dynamics of coupled optical parametric oscillators (OPOs) arising from phase-sensitive amplification and de-amplification, and show their distinct advantages over conventional non-Hermitian systems relying on laser gain and loss. OPO-based non-Hermitian systems can benefit from the instantaneous nature of the parametric gain, noiseless phase-sensitive amplification, and rich quantum and classical nonlinear dynamics. We show that two coupled OPOs can exhibit spectral anti-PT symmetry and an exceptional point between its degenerate and non-degenerate operation regimes. To demonstrate the distinct potentials of the coupled OPO system compared to conventional non-Hermitian systems, we present higher-order exceptional points with two OPOs, tunable Floquet exceptional points in a reconfigurable dynamic non-Hermitian system, and generation of squeezed vacuum around exceptional points, all of which are not easy to realize in other non-Hermitian platforms. Our results show that coupled OPOs are an outstanding non-Hermitian setting with unprecedented opportunities in realizing nonlinear dynamical systems for enhanced sensing and quantum information processing.

quant-ph↗

arXiv2020

Arbitrary linear transformations for photons in the frequency synthetic dimension

Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a new photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.

physics.optics↗

arXiv2020

$\mathcal{PT}$-Symmetric Topological Edge-Gain Effect

We demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped sub-systems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.

physics.optics↗