arXiv subjects

H. M. Bharath

Publications and source records attributed to H. M. Bharath.

13 recordsLinked to original sources

arXiv2021

Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.

cond-mat.quant-gas↗

arXiv2020

Quantum Entanglement, Symmetric Nonnegative Quadratic Polynomials and Moment Problems

Quantum states are represented by positive semidefinite Hermitian operators with unit trace, known as density matrices. An important subset of quantum states is that of separable states, the complement of which is the subset of \textit{entangled} states. We show that the problem of deciding whether a quantum state is entangled can be seen as a moment problem in real analysis. Only a small number of such moments are accessible experimentally, and so in practice the question of quantum entanglement of a many-body system can be reduced to a truncated moment problem. By considering quantum entanglement of $n$ identical atoms we arrive at the truncated moment problem defined for symmetric measures over a product of $n$ copies of unit balls in $\mathbb{R}^d$. We work with moments up to degree $2$. We derive necessary and sufficient conditions for belonging to the moment cone, which can be expressed via a linear matrix inequality of size at most $2d+2$, which is independent of $n$. The linear matrix inequalities can be converted into a set of explicit semialgebraic inequalities giving necessary and sufficient conditions for membership in the moment cone, and show that the two conditions approach each other in the limit of large $n$. The inequalities are derived via considering the dual cone of nonnegative polynomials, and its sum-of-squares relaxation. We show that the sum-of-squares relaxation of the dual cone is asymptotically exact, and using symmetry reduction techniques (J. Pure Appl. Algebra 192, no. 1-3, 95, arXiv:1205.3102), it can be written as a small linear matrix inequality of size at most $2d+2$, which is independent of $n$. For the cone of symmetric nonnegative polynomials with the relevant support we also prove an analogue of the half-degree principle for globally nonnegative symmetric polynomials (J. Math. Anal. Appl. 284, no. 1, 174, J. Pure Appl. Algebra 216, no. 4, 850).

math-ph↗

arXiv2019

Exploring Non-Abelian Geometric Phases in Spin-1 Ultracold Atoms

Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter. The geometrical and topological properties of the phase space of spin$-1$ quantum states is richer than that of spin$-1/2$ quantum states and is relatively unexplored. For instance, the spin vector of a spin-1 system, unlike that of a spin$-1/2$ system, can lie anywhere on or inside the Bloch sphere representing the phase space. Recently, a generalization of Berry's phase that encapsulates the topology of spin-1 quantum states has been formulated in J. Math. Phys., 59(6), 062105. This geometric phase includes loops that go inside the Bloch sphere and is carried by the tensor of spin fluctuations, unlike Berry's phase which is carried by the global phase of the quantum state. Furthermore, due to a mathematical singularity at the center of the Bloch sphere, the class of loops that pass through the center are called singular loops and are significant because their geometric phase is non-Abelian. In contrast with Berry's phase for spin$-1/2$ systems, whose properties come from the topology of a sphere, the properties of singular loop geometric phases come from the topology of the real projective plane $\mathbb{RP}^2$, which is more non-trivial. Here we use coherent control of ultracold $^{87}$Rb atoms in an optical trap to experimentally explore this geometric phase for singular loops in a spin-1 quantum system.

cond-mat.quant-gas↗

arXiv2018

Non-Abelian Geometric Phases Carried by the Spin Fluctuation Tensor

The expectation values of the first and second moments of the quantum mechanical spin operator can be used to define a spin vector and spin fluctuation tensor, respectively. The former is a vector inside the unit ball in three space, while the latter is represented by an ellipsoid in three space. They are both experimentally accessible in many physical systems. By considering transport of the spin vector along loops in the unit ball it is shown that the spin fluctuation tensor picks up geometric phase information. For the physically important case of spin one, the geometric phase is formulated in terms of an SO(3) operator. Loops defined in the unit ball fall into two classes: those which do not pass through the origin and those which pass through the origin. The former class of loops subtend a well defined solid angle at the origin while the latter do not and the corresponding geometric phase is non-Abelian. To deal with both classes, a notion of generalized solid angle is introduced, which helps to clarify the interpretation of the geometric phase information. The experimental systems that can be used to observe this geometric phase are also discussed.

math-ph↗

arXiv2018

Staircase in magnetization and entanglement entropy of spin squeezed condensates

Staircases in response functions are associated with physically observable quantities that respond discretely to continuous tuning of a control parameter. A well-known example is the quantization of the Hall conductivity in two dimensional electron gases at high magnetic fields. Here, we show that such a staircase response also appears in the magnetization of spin-1 atomic ensembles evolving under several spin-squeezing Hamiltonians.We discuss three examples, two mesoscopic and one macroscopic, where the system's magnetization vector responds discretely to continuous tuning of the applied magnetic field or the atom density, thus producing a magnetization staircase. The examples that we consider are directly related to Hamiltonians that have been implemented experimentally in the context of spin and spin-nematic squeezing. Thus, our results can be readily put to experimental test in spin-1 ferromagnetic $^{87}$Rb and anti-ferromagnetic $^{23}$Na condensates.

cond-mat.quant-gas↗

arXiv2015

Characterizing the energy gap and demonstrating an adiabatic quench in an interacting spin system

Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. It gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase/amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal non-equilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure their energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite size effects lead to a non-zero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.

cond-mat.quant-gas↗

arXiv2015

Kibble-Zurek Mechanism in a Spin-1 Bose-Einstein Condensate

We observe power-law scaling of the temporal onset of excitations with quench speed in the neighborhood of the quantum phase transition between the polar and broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. As the system is driven through the quantum critical point by tuning the Hamiltonian, the vanishing energy gap between the ground state and first excited state causes the reaction time scale of the system to diverge, preventing it from adiabatically following the ground state. We measure the temporal evolution of the spin populations for different quench speeds and determine the exponents characterizing the scaling of the onset of excitations, which are in good agreement with the predictions of the Kibble-Zurek mechanism.

cond-mat.quant-gas↗

arXiv2015

Quantum enhanced precision in a collective measurement

We explore the role of $\textit{collective measurements}$ on precision in estimation of a single parameter. Collective measurements are represented by observables which commute with all permutations of the probe particles. We show that with this constraint, quantum bits(qubits) outperform classical bits(non-superposable bits) in optimizing precision. Specifically, we prove that while precision in a collective measurement is loosely bounded by $O\left(\frac{1}{N}\right)$ for $N$ classical bits, using qubits it is tightly bounded by $O\left(\frac{1}{N^2}\right)$. This bound is consistent with quantum metrology protocols with the collective measurement requiring an entangled probe state to saturate. Finally, we construct a canonical measurement protocol that saturates this bound.

quant-ph↗

arXiv2014

A model independent approach towards resource count and precision limits in a general measurement

A formulation towards quantifying resource count used in a measurement, that is independent of the model of the measurement dynamics(Quantum/Classical), is considered. For any general measurement with $(M+1)$ discrete outcomes, it is found that there is a unique probability distribution that minimizes the measurement error, with the error scaling as $1/M$. For a measurement with a finite resource$(R)$, this absolute bound implies the resource count to be equal to the possible outcomes i.e. $R=M$. This formulation therefore provides a model independent route towards estimating resource count used in any general measurement scheme.

quant-ph↗

arXiv2014

Classical simulation of partially entangled states

We investigate the possibility of simulating partially entangled two qubit states by separable states of higher spins. First, we show that all partially entangled isotropic states can be simulated classically. We further investigate partially entangled pure states, and their binary mixtures and find that these systems forbid such a simulation, signifying that separability does not have a universal character in determining the inherent quantum nature of a state.

quant-ph↗

arXiv2014

Classical simulation of entangled states

Description of nonclassicality of states has hitherto been through violation of Bell inequality and non-separability, with the latter being a stronger constraint. In this paper, we show that this can be further sharpened, by introducing the concept of classical simulation. A state admits classical simulation if it can be mimicked fully by a separable state of higher dimension. A nonclassical state, which we call exceptional, does not admit classical simulation. Focusing on two qubit states, we show that exceptionality is more stringent than violation of Bell inequality, and involves an intricate interplay of coherence and entanglement. The new criterion is shown to provide a natural description of entangled states which respect Bell inequality, and also a way of enumerating the classical resources that are required to simulate a quantum state. Possible implications to quantum dynamics and quantum information are briefly touched upon.

quant-ph↗

arXiv2012

Benford's law: A theoretical explanation for base 2

In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the solutions converge to the benford's law. Finally we solve the recursion analytically to yeild the benford's law for base 2.

stat.OT↗

arXiv2010

Non-holonomic Constraint Force Postulates

The extended Hamilton's Principle and other methods proposed to handle non-holonomic constraints are considered. They dont agree with each other. By looking at its consistency with D'Alembert's principle for linear non-holonomic constraints, it was claimed in earlier papers that the direct extension of hamilton's principle is incorrect. Nonholonomic Constraints, linear in velocities were considered for this purpose. This paper analyses these claims, and shows that they are incorrect. And hence it shows that it is theoretically impossible to judge any attempt on non-holonomic constraints to be wrong, as long as they are consistent with the D'Alembertian for holonomic constraints.

physics.class-ph↗