“The behavior of things in the small scale is so fantastic! It is so wonderfully different! So marvelously different than anything that behaves on a large scale.” – Feynman
Here you will find descriptions of my current and past research, illustrated with images, slides, posters, and animations. To skip directly to publications, click here.
Position
I am a postdoctoral research associate in the Theory of Condensed Matter group at Cavendish Laboratory, University of Cambridge, working with Prof. Nigel Cooper and collaborators (ORCID). Previously, I worked as a graduate student on the theory of cold atoms with Prof. Erich Mueller at Cornell University, having explored other areas as an undergrad (see below).
Overview
Technical
My research is focused on understanding the physics of interacting quantum gases by theoretical modeling and numerical simulation. This is in part motivated by a remarkable growth of versatile experimental platforms for trapping and manipulating systems of atoms and photons (see this review). I have studied exotic phases of matter, collective excitations, and quantum dynamics of such systems. My recent work has explored novel outofequilibrium properties arising in the presence of dissipation and/or periodic driving, and how they can be probed in experiments. I am also actively involved in developing widely applicable numerical techniques, such as DMRG for continuum systems. The broad themes in my research are the following:
 Exotic quantum phases
 Collective excitations
 Nonequilibrium dynamics
 Open quantum systems
In plain English
I play with the strange mathematical rules of quantum mechanics to explore the wonderful smallscale behavior in Feynman’s quote above. Although everything is made up of these tiny objects or “atoms,” their quantum nature is often blurred by thermal fluctuations (random jiggling motion). As matter is cooled down, these fluctuations die out and one enters the quantum realm in full glory. Thanks to experimental advances, it is now possible to “cook” such scenarios in the lab and “look” at how individual particles behave. Understanding this quantum world is central to modern electronics and will play a key role in future technologies. I use a blend of analytical and numerical approaches to explore the rich features which emerge in these systems. For example, below are two articles written for a general audience: the first on ripples on a superfluid (a novel phase of matter), and the latter on “fractional” particles on a thin film of light!
 Surprising nature of quantum solitary waves revealed
 Researchers pave an enlightened path to anyons and quantum computation
Publications
 Shovan Dutta and Nigel R. Cooper, “Critical Response of a Quantum van der Pol Oscillator,” Phys. Rev. Lett. 123, 250401 (2019) [pdf] [supplement] [arXiv] [slides] [poster].
Click here to read more!
Selfsustained oscillations are ubiquitous in nature, from heartbeats to electrical circuits. Physical systems on the verge of such oscillations are incredibly sensitive to external drives and play a key role in biological sensors. For example, this is how we can hear faint whispers (see the power of hearing). In this work, we find this heightened sensitivity persists even in the microscopic world of atoms and photons, where the disparate rules of quantum mechanics dominate. An actively driven quantum oscillator not only shows enhanced sensitivity, but also exhibits surprising new features that are unique to the quantum realm. These findings could have important applications in quantum sensing and shed new insights into the outofequilibrium dynamics of quantum systems.
We model a prototypical scenario where a quantum oscillator is subject to energy dissipation. Ordinarily, the response of such oscillators is limited by damping. However, we find this limit can be negated via a strong “pump,” leading to enhanced sensitivity. Additionally, the study reveals novel features such as a regime where the response diminishes with increasing drive. These predictions can be tested in a variety of setups, e.g., atoms trapped in a well, light in a cavity, or a micromechanical membrane. Such platforms have already been used to build quantum sensors that are transforming the landscape of precision metrology and medical imaging (see https://www.bbc.co.uk/news/business47294704). Active sensing could promote further advances, yielding a “quantum ear” that can detect ultraweak signals.
 Shovan Dutta and Erich J. Mueller, “Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles,” Phys. Rev. A 97, 033825 (2018) [pdf] [supplement] [arXiv] [news story] [slides1] [slides2] [poster] [animation].
Click here to read more!
Waveparticle duality is a key principle of quantum mechanics. Central to modern electronics, it explains that matter has dual nature: “particles” like electrons can act as waves and “waves” like light can act as particles. Following new lines of research which build on this concept, we model an experimental setting where the particles of light (photons) can mimic a very special behavior of electrons in semiconductors. In particular, we show how one can use light in a cavity to create and manipulate exotic quantum excitations, known as anyons, which could form the hardware for future quantum computers. This protocol might enable the first direct probe of these exotic entities which have remained elusive.
In the protocol, the anyons are formed in the waist of an optical cavity built by carefully aligning a set of highquality mirrors. Such a setup already exists in Jon Simon’s lab in Chicago. We show how one can drive the cavity with lasers to sequentially inject photons, building up a quantum state which has vortexlike excitations with unusual properties. These excitations are the desired anyons: they act like particles, but due to their collective nature behave unlike any known elementary particle. In particular, when two of them are exchanged, the quantummechanical wavefunction gains a fractional phase. We explain how one use laser beams to create and move these anyons, and measure the fractional phase. The proposed experiment uses existing technology and can be considered the simplest “braiding” protocol, which forms the basis of topological quantum computing schemes.
 Shovan Dutta and Erich J. Mueller, “Protocol to engineer FuldeFerrellLarkinOvchinnikov states in a cold Fermi gas,” Phys. Rev. A 96, 023612 (2017) [pdf] [arXiv].
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Following up on our result in the previous paper (see below), here we propose a twostep experimental protocol to directly engineer FFLO states in a cold Fermi gas loaded into a quasi1D trap. First, one uses phase imprinting to generate a series of domain walls in a superfluid with equal number of ↑ and ↓spins. Second, one applies a controlled radiofrequency sweep which selectively breaks Cooper pairs near the domain walls and transfers the ↑spins to a third noninteracting spin state, leaving behind a stable FFLO state with one unpaired ↓spin in each domain wall. We show how the protocol can be implemented with high fidelity for a wide range of parameters available in experiments.
 Shovan Dutta and Erich J. Mueller, “Collective Modes of a Soliton Train in a Fermi Superfluid,” Phys. Rev. Lett. 118, 260402 (2017) [pdf] [arXiv] [news story] [slides] [poster].
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We study the collective motion of a train of domain walls or solitons in a quasi1D Fermi superfluid by analyzing the Bogoliubovde Gennes equations. We uncover a variety of unexpected modes, including longlived gapped modes describing oscillations of the soliton cores and an instability where pairs of solitons collide and annihilate. The instability rate is sensitive to the separation of solitons and the interaction between atoms, both of which can be tuned in experiments. In addition, the instability is prevented by magnetizing the gas – forming an exotic FFLO state which has eluded direct experimental detection despite much effort over decades. We discuss how such stable FFLO states can be directly engineered in cold Fermi gases.
 Shovan Dutta and Erich J. Mueller, “Dimensional crossover in a spinimbalanced Fermi gas,” Phys. Rev. A 94, 063627 (2016) [pdf] [arXiv] [slides].
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We study the relative stability of exotic superfluid states, such as the FFLO and breachedpair states, in a spinimbalanced Fermi gas confined in a cylindrical harmonic trap. We calculate the meanfield phase diagram in the density–imbalance plane as a function of the confinement, strength of interactions between atoms, and temperature. The phase diagram changes from 1Dlike to 3Dlike as one increases the interactions or reduces the confinement. We map the system to an effective 1D model, finding significant density dependence of the 1D scattering length. We discuss the prospects of observing the superfluid states in similar ongoing experiments.
 Shovan Dutta and Erich J. Mueller, “Kinetics of BoseEinstein condensation in a dimple potential,” Phys. Rev. A 91, 013601 (2015) [pdf] [arXiv] [slides].
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We model the dynamics of condensate formation in a bimodal optical trap, consisting of a large reservoir region and a tight, tunable “dimple” potential at the center. We simulate the quantum Boltzmann rate equations with twobody scattering and threebody loss processes to provide detailed quantitative estimates for condensate yields, lifetimes, thermalization timescales, and temperature variations. We study the dependence of these quantities with the trap parameters, explaining the principal trends in physical terms and extracting optimal parameters for future experiments.
 Shovan Dutta and Erich J. Mueller, “Variational study of polarons and bipolarons in a onedimensional Bose lattice gas in both the superfluid and the Mottinsulator regimes,” Phys. Rev. A 88, 053601 (2013) [pdf] [arXiv] [slides].
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We model the spread of an impurity in a 1D Bose gas across the SuperfluidMott transition through a computationally tractable variational ansatz. When the interactions between atoms are strong, we find the impurity binds with a hole, forming a quasiparticle known as a polaron. We characterize the dynamics and stability of this polaron and explain the features observed in a recent experiment. We find that two polarons can bind together to form a bipolaron. At weaker interactions, the polaron becomes unstable over a growing range of momentum and decays into particlehole excitations. We predict how this instability can be observed in experiments by measuring the impurityhole correlation.
Eprints
 Shovan Dutta, “Collective Phenomena in Quantum Gases,” PhD thesis (2018).
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Motivated by rapid experimental progress in the fields of ultracold atoms and quantum optics, I present a series of theoretical studies which explore collective phenomena in quantum gases of atoms and photons. In Chapter 1, I highlight the major developments in the research field and identify the overarching themes and motivations. I also provide a roadmap for the rest of the thesis and summarize the main results. The remaining eight chapters contain original studies, organized along three broad motifs. In Chapters 2 through 5, I investigate how the nature of collective excitations and quasiparticles can be explored in modern experiments. More specifically, I model the dynamics of a spin impurity in a Bose lattice gas, develop a protocol for observing fractionalized excitations or anyons in an optical cavity, and characterize the collective dynamics of Bogoliubov quasiparticles and domain walls in a Fermi superfluid. In Chapters 6 and 7, I examine unconventional superfluid phases in spinimbalanced Fermi gases. In particular, I propose a novel technique for engineering the longsoughtafter FuldeFerrellLarkinOvchinnikov (FFLO) phase and study the relative stability of exotic phases across a dimensional crossover. Finally, Chapters 8 and 9 are devoted to studies of kinetics in outofequilibrium systems. I model the formation of a BoseEinstein condensate in a dimple trap and characterize the approach to thermal equilibrium in quasionedimensional geometries.
 Shovan Dutta and Subhankar Ray, “Damped bead on a rotating circular hoop – a bifurcation zoo,” arXiv:1201.1218 (2012) [slides].
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We investigate the evergreen problem of bead on a rotating hoop, but with damping. The introduction of damping alters the nature of the fixed points, giving rise to a multitude of new bifurcations. We show phase portraits and trajectories corresponding to different motions of the bead, characterizing its dynamics over the full parameter space. For certain critical values of the damping coefficient and rotation speed, linear stability analysis is insufficient to classify the nature of the fixed points. We present a rigorous technique involving transformation of coordinates and order of magnitude arguments to resolve such cases, which might provide a general framework to treat such borderline cases in more complex nonlinear systems.
 Shovan Dutta and Subhankar Ray, “Bead on a rotating circular hoop: a simple yet featurerich dynamical system,” arXiv:1112.4697 (2011).
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We perform an indepth analysis of the nonlinear dynamics of an undamped bead on a rotating hoop using elementary calculus and symmetry arguments. We characterize the different types of motion the bead can undergo and show simulations of its beautiful trajectories. At a critical rotation speed, the system undergoes a pitchfork bifurcation where two new equilibrium points emerge on either side of the hoop. We find a dramatic change in the relation between time period and amplitude of bead oscillations as the rotation speed is varied. The study would be particularly useful to students as it illustrates such concepts as phase portraits, bifurcations, symmetry breaking, critical slowing down, and the use of Lagrange multipliers to determine constraint forces.
 Shovan Dutta, Subhankar Ray, and J. Shamanna, “Continuous Time Random Walk with timedependent jump probability: a direct probabilistic approach,” arXiv:1112.3253 (2011).
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We tackle the problem of a continuoustime random walk in 3D under timevarying external fields: the random walker, on arriving at position ρ at time τ, stays there for a time t´, after which it jumps to a new position at time t = τ + t´. The waiting time t´ is distributed with a probability density function ψ(t´). The probability that a jump occurring at time t results in a displacement between r´ and r´ + dr´ is φ(r´t) d^{3}r´. The goal is to find the probability density p(r,t) that the random walker is at position r at time t. Continuoustime random walks are good models of anomalous diffusion.
We use direct probability arguments to derive recurrence relations for all moments of p(r,t) for arbitrary choices of ψ(t´) and φ(r´t). For a memoryless walk, where ψ(t´) is exponential, we simplify these equations further to find a closed form expression for p(r,t). We also consider the special case of a 1D lattice with nearestneighbor jumps, which was modeled in prior work by a Fractional FokkerPlanck Equation (FFPE). Our equations reproduce the mean and standard deviation in the FFPE formulation but has additional terms for the higher moments which can markedly alter the asymmetry (skewness) and peakedness (kurtosis) of p(r,t). We show that the missing terms are an artifact of the approximation in taking the continuum limit to derive the FFPE.
 Shovan Dutta, “A simple circuit model showing featurerich BogdanovTakens bifurcation,” IEEE link [best paper in National Students Paper and Circuit Design Contest (NSPCDC) 2011].
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I propose an easytoimplement circuit model for the BogdanovTakens bifurcation, exhibiting three local (spiraltonode, saddlenode, AndronovHopf) and one global (Homoclinic) bifurcations. The bifurcations have a profound effect on the system stability. For example, in the Homoclinic bifurcation, a stable limit cycle collides with a saddle and disappears. Thus the physical variables such as currents and voltages executing sustained oscillations suddenly increase in an unbounded manner. Such dramatic changes are useful in describing voltage collapse in power systems, excitability of neurons, and several other phenomena. With the proposed circuit, one can experimentally measure the drastic changes in the dynamics simply by altering the values of some linear circuit elements.
Work in progress
 Hardcore bosons with local source and sink [with Nigel Cooper].
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With the recent experimental demonstration of a Mott insulator of photons (Nature 2019), local sources and sinks allow for the exciting prospect of driving strongly interacting photon currents and study the interplay between interactions and dissipation. We find, surprisingly, that the dissipation can produce longrange correlated particlehole pairs in steady state (over a thermal background). Furthermore, for certain simple sourcesink configurations, there can be multiple steady states with longrange entanglement! These steady states have analytic solutions (in 1D), even though the system cannot be reduced to free fermions by a JordanWigner transformation.
 Dynamically induced insulatorsuperfluid transitions by resonant shaking [with Ulrich Schneider and Nigel Cooper].
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We have all seen wine glasses being shattered by a high pitch! The resonant sound excites increasingly strong vibrations in the glass until the glass order is broken. Here we study a scenario where one can resonantly shake an insulator and turn it into a superfluid.
Consider bosonic atoms loaded into an optical lattice. One can control the tunneling between lattice sites by changing the lattice depth. When the atoms are in the lowest band, it is well known that they form an insulator for weak tunneling, and a superfluid for strong tunneling. However, one can also increase the effective tunneling by coupling the atoms to a higher band, e.g. by resonantly shaking the lattice. Thus, it is possible to start with an insulator in the lowest band and then cause it to melt simply by turning on this shaking. We’re studying the various phase transitions which are possible under this controllable dynamical setting.
 Matrix product states (DMRG) for continuous 1D systems [with Erich Mueller (Cornell), Anton Buyskikh (Riverlane), and Andrew Daley (Strathclyde)].
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What prohibits the exact simulation of large quantum systems is that the space of all possible states grows exponentially with the system size. For discrete 1D systems, the “Density Matrix Renormalization Group” (DMRG) technique provides a viable solution by letting one systematically truncate this space based on the degree of entanglement between subsystems. Indeed, DMRG cast in terms of Matrix Product States is the state of the art for simulating such systems. There has been attempts to generalize this technique to continuous systems, but they have severe limitations for nonhomogeneous or timedependent settings.
We’re developing a new algorithm which allows one to study continuum systems via the standard DMRG/TEBD techniques, without distorting the physics with an artificial lattice. In brief, one divides the system up into multiple segments, describing the local physics with fewbody wave functions while imposing continuity across neighboring segments. We wish to apply this framework to studying a number of topical problems.
Talks
 2019
 “Critical Response of a Quantum van der Pol Oscillator,” Centre for Condensed Matter Theory (CCMT) Seminar, Indian Institute of Science (IISc), December 11, 2019.
 “Critical Response of a Quantum van der Pol Oscillator,” Joint DesOEQQSUM meeting, University of Oxford, September 16, 2019.
 “Critical Response of a Quantum van der Pol Oscillator,” Collective Phenomena Group Meeting (CPGM) talk, University of Cambridge, July 16, 2019.
 “Critical Response of a Quantum van der Pol Oscillator,” Condensed Matter and Quantum Materials (CMQM) Conference, University of St Andrews, July 03, 2019.
 “Paving an enlightened path to anyons and quantum computation,” Science Lunchtime Seminar, Darwin College, Cambridge, April 25, 2019.
 “Creating and Braiding Anyons in an Optical Cavity,” Department of Physics Seminar, University of Strathclyde, January 2019.
 2018
 “Creating and Braiding Anyons in an Optical Cavity,” Collective Phenomena Group Meeting (CPGM) talk, University of Cambridge, October 10, 2018.
 “Creating and Braiding Anyons in an Optical Cavity,” Public talk (thesis defense), Department of Physics, Cornell University, April 27, 2018.
 2017
 “Collective Dynamics of Solitons in Superfluids,” Research highlight for prospective graduate students, Department of Physics, Cornell University, March 27, 2017.
Posters
 2019
 “Critical Response of a Quantum van der Pol Oscillator,” BoseEinstein Condensation (BEC) 2019, Sant Feliu de Guixols, Spain, September 09, 2019.
 “Creating and Braiding Anyons in an Optical Cavity,” MPIPKS International Workshop on Synthetic Topological Matter, Dresden, Germany, May 21, 2019.
 “Critical Response of a Quantum van der Pol Oscillator,” DesOEQ (Designing OutofEquilibrium Quantum systems) Review Meeting, Glasgow, Scotland, March 14, 2019.
 2018
 “Creating and Braiding Anyons in an Optical Cavity,” DesOEQ Annual Meeting & DOQS Workshop, Glasgow, Scotland, October 15, 2018.
 “Creating and Braiding Anyons in an Optical Cavity,” 49th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (DAMOP), Fort Lauderdale, Florida, May 30, 2018.
 “Creating and Braiding Anyons in an Optical Cavity,” Cornell Center for Materials Research (CCMR) Symposium on Advances in Photonics and Quantum Optics, Ithaca, New York, May 23, 2018.
 2017
 “Creating and Braiding Anyons in an Optical Cavity,” ARO/AFOSR Quantum Matter MURI Program Review, Gaithersburg, Maryland, October 12, 2017.
 “Creating and Braiding Anyons in an Optical Cavity,” ITAMP workshop on ManyBody Cavity QED, Boston, Massachusetts, October 10, 2017.
 “Collective Modes of a Soliton Train in a Fermi Superfluid,” 48th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics (DAMOP), Sacramento, California, June 6, 2017.
 2016
 “Collective Modes of a Soliton Train in a Fermi Superfluid,” ARO/AFOSR Quantum Matter MURI Program Review, Chicago, Illinois, September 27, 2016.
Unpublished work
 Understanding a longstanding puzzle in liquid Helium3: How does the superfluid B phase nucleate in the supercooled liquid? (2018) [with Erich Mueller and Jeevak Parpia].
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Cut a long story (see below) short: the puzzle is still open as ever! We tried sophisticated approaches for finding the nucleation energy, such as the nudged elastic band method, but that did not explain the observations.
Helium is one of the few elements which refuses to solidify at normal pressure no matter how much it is cooled. This is a consequence of the Heisenberg uncertainty principle of quantum mechanics which prevents everything from coming to a standstill even at absolute zero temperature. The residual energy, called the zeropoint energy, is larger for lighter elements like Helium. Moreover, being a noble gas, the interatomic forces in helium are weak — too weak, in fact, to lock the atoms into a regular grid and form a solid. So it remains a liquid even at absolute zero. But that is only the start – the story gets much more interesting!
There are two stable isotopes of Helium: He3 and He4. As early as 1937, He4 was cooled below a few K, where it suddenly became a superfluid, displaying some bizarre properties! On the other hand, He3 remained a rather “boring” liquid even at much lower temperatures. But in November 1971, in a cold Ithaca winter (~250 K), He3 was cooled much further (~2 mK), and lo! It turned superfluid. Not only that, two different types of superfluid — called rather unimaginatively “A” and “B” 🙂 . This vast difference between the two isotopes has its origin in quantum statistics. He4 has an even number of fermions (protons, neutrons, and electrons), so it obeys Bose statistics. Conversely, He3 has an odd number of fermions and obeys Fermi statistics. And that makes all the difference. Whereas bosons can condense into the same state at low temperatures, fermions have to pair up before they can condense. This Cooper pairing occurs at much lower temperatures, and depending on the internal structure of the pairs, He3 can form different superfluid states which are much more exotic than the structureless superfluid of He4! Read this entertaining review.
Now comes the puzzle: the superfluid A phase is stable only above a critical temperature, below which the superfluid B phase is stable (see phase diagram). However, He3 can be “supercooled” below this critical temperature and still remain in the A phase. Now, the puzzle comes in how the liquid eventually turns into the B phase as it is cooled further. Experiments have seen such nucleation of the B phase, but we still don’t understand the mechanism! Despite some rather crazy proposals, there is yet no definitive theoretical understanding which explains this nucleation phenomena. However, new experiments underway in Jeevak Parpia’s lab at Cornell.
 1Dto3D crossover in the superfluidity of a spinimbalanced Fermi gas in an array of coupled tubes (2016) [with Erich Mueller].
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This is an extension of our work on dimensional crossover in a cylindrically confined spinimbalanced Fermi gas (see above). Here we consider a 3D gas broken up into tubes by a 2D lattice, as in experiments at Rice, and calculate the (BdG) phase diagram taking into account the higher energy bands. The 1Dto3D crossover occurs in two different manner depending on whether the lattice depth is decreased or the interactions are increased. For weak interactions, when the (average) chemical potential lies within an energy band, we find 3Dlike behavior, whereas if the chemical potential lies between the 1st and 2nd band, we find 1D like behavior. As the lattice depth is decreased, these features are qualitatively unchanged, however the energy bands get wider and eventually the spectrum becomes gapless, making the entire phase diagram 3D like. On the other hand, stronger interactions cause mixing between the energy bands and the 1Dlike behavior is suppressed.

Note: In the figures, gray regions indicate locations of the energy bands. Some of the figures only show the critical imbalance for the BCS state. Generically the region just outside is FFLO. The curve has a positive slope in 3D and a negative slope in 1D.
 Thermalization in a quasionedimensional quantum gas (2015) [with Erich Mueller and Mukund Vengalattore] [manuscript] [slides].
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We model thermalization in a quantum gas via binary elastic collisions after the gas is loaded into an array of weaklycoupled 1D tubes by turning on an optical lattice in the transverse plane. When the lattice is turned on adiabatically (slow compared to the collision rate), the quasimomentum distribution evolves smoothly into a thermal profile. For small intertube coupling J, the rate of thermalization grows as J^{2} log J. We show that the equilibration times in two recent experiments [Nature 467, 567 (2010)] and [Nature 440, 900 (2006)] differ hugely from one another, which explains why one of them saw a thermal cloud whereas the other didn’t. When the lattice is turned on suddenly (fast compared to the collision rate), the momentum distribution develops multiple isolated peaks which eventually merge into a thermal distribution. These nonequilibrium peaks originate from the exchange of particles between different energy bands and can be resolved for about 50 collision times.
Undergraduate research
 Bifurcation in classical dynamical systems [with Subhankar Ray]: Exploring simple nonlinear systems with featurerich bifurcation diagrams, coming up with techniques to characterize borderline cases where linear stability analysis fails (see eprints above).
 Random walks modeling anomalous diffusion [with Subhankar Ray and Jaya Shamanna]: Using probability arguments and integrodifferential equations to model a continuoustime random walk under an external field, leading to subdiffusive transport (see eprint above).
 Photoemission from thin films [with Manas Bose and Chayanika Bose]: Using Boltzmann rate equations to model photocurrent from a semiconductor film as a function of the film thickness and the frequency and polarization of incident light (senioryear project).
 PTsymmetric quantum mechanics [with Subhankar Ray]: Exploring the properties of a class of nonHermitian Hamiltonians that are symmetric under spacetime reflection, and their equivalence to Hermitian Hamiltonians used in ordinary quantum mechanics.
 Liquidgas phase transition of nuclear matter [with Subhankar Ray and Jaya Shamanna]: Using the BethePeierls approximation to model the liquidgas phase transition in a cubic lattice gas model of cold nuclear matter.
Other activities
 Editorial: Referee for Physical Review Letters (since 2017), Physical Review A (since 2018), and Physical Review B (since 2019).
 Administrative: Coorganizer for the Cavendish Quantum Colloquia 201819, University of Cambridge.
 Teaching: Served as teaching assiatnt and supervisor for several undergraduate courses at Cornell and Cambridge. Please see the Teaching page for details.