Arindam Mallick
@zoa.ift.uj.edu.pl
Assistant Professor (Postdoc) / Quantum Simulations Group / Atomic Optics Department, Institute of Theoretical Physics, Jagiellonian University in Krakow ul. Lojasiewicza 11, 30-348 Kraków, Poland
Jagiellonian University in Krakow ul. Lojasiewicza 11, 30-348 Kraków, Poland
RESEARCH, TEACHING, or OTHER INTERESTS
Condensed Matter Physics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics, Nuclear and High Energy Physics
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Scopus Publications
Arindam Mallick and Jakub Zakrzewski
American Physical Society (APS)
Quantum simulators of lattice gauge theories involve dynamics of typically short-ranged interacting particles and dynamical fields. Elimination of the latter via Gauss law leads to infinite range interactions as exemplified by the Schwinger model in a staggered formalism. This motivates the study of long-range interactions, not necessarily diminishing with the distance. Here we consider localization properties of a spin chain with interaction strength growing linearly along the chain as for the Schwinger model. We generalize the problem to models with different interaction ranges. Using exact diagonalization we find the participation ratio of all eigenstates, which allows us to quantify the localization volume in Hilbert space. Surprisingly, the localization volume changes nonmonotonically with the interaction range. Our study is relevant for quantum simulators of lattice gauge theories implemented in state-of-the-art cold atom/ion devices, and it could help to reveal hidden features in disorder-free confinement phenomena in long-range interacting systems.
Arindam Mallick, Alexei Andreanov, and Sergej Flach
American Physical Society (APS)
We demonstrate the existence of an intermediate super-exponential localization regime for eigenstates of the Aubry-Andr\\'e chain. In this regime, the eigenstates localize factorially similarly to the eigenstates of the Wannier-Stark ladder. The super-exponential decay emerges on intermediate length scales for large values of the $\\textit{winding length}$ -- the quasi-period of the Aubry-Andr\\'e potential. This intermediate localization is present both in the metallic and insulating phases of the system. In the insulating phase, the super-exponential localization is periodically interrupted by weaker decaying tails to form the conventional asymptotic exponential decay predicted for the Aubry-Andr\\'e model. In the metallic phase, the super-exponential localization happens for states with energies away from the center of the spectrum and is followed by a super-exponential growth into the next peak of the extended eigenstate. By adjusting the parameters it is possible to arbitrarily extend the validity of the super-exponential localization. A similar intermediate super-exponential localization regime is demonstrated in quasiperiodic discrete-time unitary maps.
Arindam Mallick, Alexei Andreanov, and Sergej Flach
American Physical Society (APS)
Tight-binding single-particle models on simple Bravais lattices in space dimension d ≥ 2, when exposed to commensurate DC fields, result in the complete absence of transport due to the formation of Wannier–Stark flatbands [Phys. Rev. Res. 3 , 013174 (2021)]. The single-particle states localize in a factorial manner, i.e., faster than exponential. Here, we introduce interaction among two such particles that partially lifts the localization and results in metallic two-particle bound states that propagate in the directions perpendicular to the DC field. We demonstrate this effect using a square lattice with Hubbard interaction. We apply perturbation theory in the regime of interaction strength ( U ) (cid:28) hopping strength ( t ) (cid:28) field strength ( F ), and obtain estimates for the group velocity of the bound states in the direction perpendicular to the field. The two-particle group velocity scales as U ( t/ F ) ν . We calculate the dependence of the exponent ν on the DC field direction and on the dominant two-particle configurations related to the choices of unperturbed flatbands. Numerical simulations confirm our predictions from the perturbative analysis.
Arindam Mallick, Nana Chang, Alexei Andreanov, and Sergej Flach
American Physical Society (APS)
We consider tight-binding single particle lattice Hamiltonians which are invariant under an antiunitary antisymmetry: the anti-$\\mathcal{PT}$ symmetry. The Hermitian Hamiltonians are defined on $d$-dimensional non-Bravais lattices. For an odd number of sublattices, the anti-$\\mathcal{PT}$ symmetry protects a flatband at energy $E = 0$. We derive the anti-$\\mathcal{PT}$ constraints on the Hamiltonian and use them to generate examples of generalized kagome networks in two and three lattice dimensions. Furthermore, we show that the anti-$\\mathcal{PT}$ symmetry persists in the presence of uniform DC fields and ensures the presence of flatbands in the corresponding irreducible Wannier-Stark band structure. We provide examples of the Wannier-Stark band structure of generalized kagome networks in the presence of DC fields, and their implementation using Floquet engineering.
Arindam Mallick and Sergej Flach
American Physical Society (APS)
Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length ξ. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by (i) using the ultrafast unitary Floquet dynamics of discretetime quantum walks, (ii) an interaction strength ramping to speed up the subdiffusion, and (iii) an action discretization of the nonlinear terms. We observe the saturation of the cloud expansion of N particles to a volume ∼ Nξ. We predict and observe a universal intermediate logarithmic expansion regime which connects the mean-field diffusion with the final saturation regime and is entirely controlled by particle number N . The temporal window of that regime grows exponentially with the localization length ξ.
Arindam Mallick, Nana Chang, Wulayimu Maimaiti, Sergej Flach, and Alexei Andreanov
American Physical Society (APS)
We systematically construct flatbands for tight-binding models on simple Bravais lattices in space dimension $d \\geq 2$ in the presence of a static uniform DC field. Commensurate DC field directions yield irreducible Wannier-Stark bands in perpendicular dimension $d-1$ with $d$-dimensional eigenfunctions. The irreducible bands turn into dispersionless flatbands in the absence of nearest neighbor hoppings between lattice sites in any direction perpendicular to the DC field one. The number of commensurate directions which yield flatbands is of measure one. We arrive at a complete halt of transport, with the DC field prohibiting transport along the field direction, and the flatbands prohibiting transport in all perpendicular directions as well. The anisotropic flatband eigenstates are localizing at least factorially (faster than exponential).
János K. Asbóth and Arindam Mallick
American Physical Society (APS)
We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states. Spatial disorder can lead to Anderson localization, inhibiting the spread of quantum walks, putting them at a disadvantage against their diffusively spreading classical counterparts. We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization, but to a diffusive spread instead. This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We base this explanation on the relationship of this general quantum walk to a simpler case more studied in the literature, and for which disorder-induced delocalization of a topological origin has been observed. We review topological delocalization for the simpler quantum walk, using time-evolution of the wavefunctions and level spacing statistics. We apply scattering theory to two-dimensional quantum walks, and thus calculate the topological invariants of disordered quantum walks, substantiating the topological interpretation of the delocalization, and finding signatures of the delocalization in the finite-size scaling of transmission. We show criticality of the Haar random quantum walk by calculating the critical exponent $\\eta$ in three different ways, and find $\\eta$ $\\approx$ 0.52 as in the integer quantum Hall effect. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.
Arindam Mallick, Thudiyangal Mithun, and Sergej Flach
American Physical Society (APS)
We numerically investigate the quench expansion dynamics of an initially confined state in a two-dimensional Gross-Pitaevskii lattice in the presence of external disorder. The expansion dynamics is conveniently described in the control parameter space of the energy and norm densities. The expansion can slow down substantially if the expected final state is a non-ergodic non-Gibbs one, regardless of the disorder strength. Likewise stronger disorder delays expansion. We compare our results with recent studies for quantum many body quench experiments.
A. Mallick, M. V. Fistul, P. Kaczynska, and S. Flach
American Physical Society (APS)
We predict and theoretically study in detail the ratchet effect for the spectral magnetization of periodic discrete time quantum walks (DTQWs) --- a repetition of a sequence of $m$ different DTQWs. These generalized DTQWs are achieved by varying the corresponding coin operator parameters periodically with discrete time. We consider periods $m=1,2,3$. The dynamics of $m$-periodic DTQWs is characterized by a two-band dispersion relation $\\omega^{(m)}_{\\pm}(k)$, where $k$ is the wave vector. We identify a generalized parity symmetry of $m$-periodic DTQWs. The symmetry can be broken for $m=2,3$ by proper choices of the coin operator parameters. The obtained symmetry breaking results in a ratchet effect, i.e. the appearance of a nonzero spectral magnetization $M_s(\\omega)$. This ratchet effect can be observed in the framework of continuous quantum measurements of the time-dependent correlation function of periodic DTQWs.
Sagnik Chakraborty, Arindam Mallick, Dipanjan Mandal, Sandeep K. Goyal, and Sibasish Ghosh
Springer Science and Business Media LLC
An amendment to this paper has been published and can be accessed via a link at the top of the paper.
Sagnik Chakraborty, Arindam Mallick, Dipanjan Mandal, Sandeep K. Goyal, and Sibasish Ghosh
Springer Science and Business Media LLC
AbstractThe question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the ‘spin bath’ model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.
Arindam Mallick, Sanjoy Mandal, Anirban Karan, and C M Chandrashekar
IOP Publishing
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete form. In this work, starting from a modified version of one-spatial dimensional general inhomogeneous split-step discrete quantum walk we derive an effective Hamiltonian which mimics a single massive Dirac particle dynamics in curved (1 + 1) space-time dimension coupled to U(1) gauge potential—which is a forward step towards the simulation of the unification of electromagnetic and gravitational forces in lower dimension and at the single particle level. Implementation of this simulation scheme in simple qubit-system has been demonstrated. We show that the same Hamiltonian can represent (2 + 1) space-time dimensional Dirac particle dynamics when one of the spatial momenta remains fixed. We also discuss how we can include U(N) gauge potential in our scheme, in order to capture other fundamental force effects on the Dirac particle. The emergence of curvature in the two-particle split-step quantum walk has also been investigated while the particles are interacting through their entangled coin operation.
Arindam Mallick and Sibasish Ghosh
American Physical Society (APS)
Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information. But such a detection should be made in a device independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement device independent way [Phys. Rev. Lett {\\bf 110}, 060405 (2013)] does require information about the state. Here by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A {\\bf 77}, 030301 (2008)], we provide a universal detection scheme for two-qubit states in a measurement device independent way. We provide a set of universal witness operators for detecting NPT-ness(negative under partial transpose) of states in a measurement device independent way. We conjecture that no such universal entanglement witness exists for PPT(positive under partial transpose) entangled states. We also analyse the robustness of some of the experimental schemes of detecting entanglement in a measurement device independent way under the influence of noise in the inputs (from the referee) as well as in the measurement operator as envisazed in ref. [Phys. Rev. Lett {\\bf 110}, 060405 (2013)].
Sagnik Chakraborty, Arpan Das, Arindam Mallick, and C. M. Chandrashekar
Wiley
Symmetrically evolving discrete quantum walk results in dynamic localization with zero mean displacement when the standard evolution operations are replaced by a temporal disorder evolution operation. In this work we show that the quantum ratchet action, that is, a directed transport in standard or disordered discrete‐time quantum walk can be realized by introducing a pawl like effect realized by using a fixed coin operation at marked positions that is, different from the ones used for evolution at other positions. We also show that the combination of standard and disordered evolution operations can be optimized to get the mean displacement of order ∝ t (number of walk steps). This model of quantum ratchet in quantum walk is defined using only a set of entangling unitary operators resulting in the coherent quantum transport.
Arindam Mallick, Sanjoy Mandal, and C. M. Chandrashekar
Springer Science and Business Media LLC
Arindam Mallick and C. M. Chandrashekar
Springer Science and Business Media LLC
AbstractSimulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.