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Wojciech H. Zurek

Publications and source records attributed to Wojciech H. Zurek.

At least 73 records · Page 4Linked to original sources
arXiv2011

Winding up superfluid in a torus via Bose Einstein condensation

We simulate Bose-Einstein condensation (BEC) in a ring employing stochastic Gross-Pitaevskii equation and show that cooling through the critical temperature can generate spontaneous quantized circulation around the ring of the newborn condensate. Dispersion of the resulting winding numbers follows scaling law predicted by the Kibble-Zurek mechanism (KZM). Density growth also exhibits scaling behavior consistent with KZM. This paves a way towards experimental verification of KZM scalings, and experimental determination of critical exponents for the BEC transition.

cond-mat.other↗
arXiv2010

Causality in Condensates: Grey Solitons as Remnants of BEC Formation

Symmetry breaking during phase transitions can lead to the formation of topological defects (such as vortex lines in superfluids). However, the usually studied BEC's have the shape of a cigar, a geometry that impedes vortex formation, survival, and detection. I show that, in elongated traps, one can expect the formation of "grey solitons" (long-lived, non-topological "phase defects") as a result of the same mechanism. Their number will rise approximately in proportion to the transition rate. This steep rise is due to the increasing size of the region of the BEC cigar where the phase of the condensate wavefunction is chosen locally (rather than passed on from the already formed BEC).

cond-mat.stat-mech↗
arXiv2010

Quantum Darwinism in an Everyday Environment: Huge Redundancy in Scattered Photons

We study quantum Darwinism--the redundant recording of information about the preferred states of a decohering system by its environment--for an object illuminated by a black body. In the cases of point-source and isotropic illumination, we calculate the quantum mutual information between the object and its photon environment. We demonstrate that this realistic model exhibits fast and extensive proliferation of information about the object into the environment and results in redundancies orders of magnitude larger than the exactly soluble models considered to date.

quant-ph↗
arXiv2010

Information Distance

While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two pictures. We give several natural definitions of a universal information metric, based on length of shortest programs for either ordinary computations or reversible (dissipationless) computations. It turns out that these definitions are equivalent up to an additive logarithmic term. We show that the information distance is a universal cognitive similarity distance. We investigate the maximal correlation of the shortest programs involved, the maximal uncorrelation of programs (a generalization of the Slepian-Wolf theorem of classical information theory), and the density properties of the discrete metric spaces induced by the information distances. A related distance measures the amount of nonreversibility of a computation. Using the physical theory of reversible computation, we give an appropriate (universal, anti-symmetric, and transitive) measure of the thermodynamic work required to transform one object in another object by the most efficient process. Information distance between individual objects is needed in pattern recognition where one wants to express effective notions of "pattern similarity" or "cognitive similarity" between individual objects and in thermodynamics of computation where one wants to analyse the energy dissipation of a computation from a particular input to a particular output.

cs.IT↗
arXiv2010

Quantum Darwinism in non-ideal environments

Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, E, is in a non-ideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, S, and an environment fragment, F, is given solely by F's entropy increase. This demonstrates that the environment's capacity for recording the state of S is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with S, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that - when decoherence is not complete - the deviation of the mutual information from F's entropy change is quantified by the quantum discord, i.e., the excess mutual information between S and F is information regarding the initial coherence between pointer states of S. In addition to illustrating these results with a single qubit system interacting with a multi-qubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of S. Our results demonstrate that Quantum Darwinism is robust with respect to non-ideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.

quant-ph↗
arXiv2010

Soliton creation during a Bose-Einstein condensation

We use stochastic Gross-Pitaevskii equation to study dynamics of Bose-Einstein condensation. We show that cooling into a Bose-Einstein condensate (BEC) can create solitons with density given by the cooling rate and by the critical exponents of the transition. Thus, counting solitons left in its wake should allow one to determine the critical exponents z and nu for a BEC phase transition. The same information can be extracted from two-point correlation functions.

cond-mat.quant-gas↗
arXiv2009

Quantum Darwinism in a hazy environment

Quantum Darwinism recognizes that we - the observers - acquire our information about the "systems of interest" indirectly from their imprints on the environment. Here, we show that information about a system can be acquired from a mixed-state, or hazy, environment, but the storage capacity of an environment fragment is suppressed by its initial entropy. In the case of good decoherence, the mutual information between the system and the fragment is given solely by the fragment's entropy increase. For fairly mixed environments, this means a reduction by a factor 1-h, where h is the haziness of the environment, i.e., the initial entropy of an environment qubit. Thus, even such hazy environments eventually reveal the state of the system, although now the intercepted environment fragment must be larger by ~1/(1-h) to gain the same information about the system.

quant-ph↗
arXiv2009

Quantum phase transition in space in a ferromagnetic spin-1 Bose-Einstein condensate

A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose-Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e., the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent nu.

cond-mat.stat-mech↗
arXiv2008

Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?

We extend the theory of symmetry breaking dynamics in non-equilibrium second order phase transitions known as the Kibble-Zurek mechanism (KZM) to transitions where the change of phase occurs not in time, but in space. This can be due to a time-independent spatial variation of a field that imposes a phase with one symmetry to the left of where it attains critical value, while allowing spontaneous symmetry breaking to the right of that critical borderline. Topological defects need not form in such a situation. We show, however, that the size, in space, of the ``scar'' over which the order parameter adjusts as it ``bends'' interpolating between the phases with different symmetry follows from a KZM - like approach. As we illustrate on the example of a transverse quantum Ising model, in quantum phase transitions this spatial scale -- the size of the scar -- is directly reflected in the energy spectrum of the system: In particular, it determines the size of the energy gap.

cond-mat.stat-mech↗
arXiv2008

How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate

We discuss the dynamics of a quantum phase transition in a spin-1 Bose-Einstein condensate when it is driven from the magnetized broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We determine where the condensate goes out of equilibrium as it approaches the critical point, and compute the condensate magnetization at the critical point. This is done within a quantum Kibble-Zurek scheme traditionally employed in the context of symmetry-breaking quantum phase transitions. Then we study the influence of the nonequilibrium dynamics near a critical point on the condensate magnetization. In particular, when the quench stops at the critical point, nonlinear oscillations of magnetization occur. They are characterized by a period and an amplitude that are inversely proportional. If we keep driving the condensate far away from the critical point through the unmagnetized ``symmetric'' polar phase, the amplitude of magnetization oscillations slowly decreases reaching a non-zero asymptotic value. That process is described by the equation that can be mapped onto the classical mechanical problem of a particle moving under the influence of harmonic and ``anti-friction'' forces whose interplay leads to surprisingly simple fixed-amplitude oscillations. We obtain several scaling results relating the condensate magnetization to the quench rate, and verify numerically all analytical predictions.

cond-mat.other↗
arXiv2007

Quantum Darwinism in quantum Brownian motion: the vacuum as a witness

We study quantum Darwinism -- the redundant recording of information about a decohering system by its environment -- in zero-temperature quantum Brownian motion. An initially nonlocal quantum state leaves a record whose redundancy increases rapidly with its spatial extent. Significant delocalization (e.g., a Schroedinger's Cat state) causes high redundancy: many observers can measure the system's position without perturbing it. This explains the objective (i.e. classical) existence of einselected, decoherence-resistant pointer states of macroscopic objects.

quant-ph↗
arXiv2007

Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model

Quantum Ising model in one dimension is an exactly solvable example of a quantum phase transition. We investigate its behavior during a quench from a paramagnetic to ferromagnetic phase caused by a gradual turning off of the transverse field at a fixed rate characterized by the quench time $τ_Q$. In agreement with Kibble-Zurek mechanism, quantum state of the system after the transition exhibits a characteristic correlation length $\hatξ$ proportional to the square root of the quench time $τ_Q$. The inverse of this correlation length determines average density of defects after the transition. In this paper, we show that $\hatξ$ also controls the entropy of entanglement of a block of $L$ spins with the rest of the system. For large $L$, this entropy saturates at $\frac16\log_2\hatξ$, as might have been expected from the Kibble-Zurek mechanism. Close to the critical point, the entropy saturates when the block size $L\approx\hatξ$, but -- in the subsequent evolution in the ferromagnetic phase -- a somewhat larger length scale $l=\sqrt{τ_Q}\lnτ_Q$ develops as a result of quantum dephasing, and the entropy saturates when $L\approx l$. We also study the spin-spin correlation. We find that close to the critical point ferromagnetic correlations decay exponentially with the dynamical correlation length $\hatξ$, but in the following evolution this correlation function becomes oscillatory at distances less than this scale. However, both the wavelength and the correlation length of these oscillations are still determined by $\hatξ$. We also derive probability distribution for the number of kinks in a finite spin chain after the transition.

cond-mat.str-el↗
arXiv2006

Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid

We study the dynamics of phase transitions in the one dimensional Bose-Hubbard model. To drive the system from Mott insulator to superfluid phase, we change the tunneling frequency at a finite rate. We investigate the build up of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.

cond-mat.other↗
arXiv2006

Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again

We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener like problems.

cond-mat.other↗
arXiv2006

Dynamics of a Quantum Phase Transition

We present two approaches to the dynamics of a quench-induced phase transition in quantum Ising model. The first one retraces steps of the standard approach to thermodynamic second order phase transitions in the quantum setting. The second one is purely quantum, based on the Landau-Zener formula for transition probabilities in avoided level crossings. We show that the two approaches yield compatible results for the scaling of the defect density with the quench rate. We exhibit similarities between them, and comment on the insights they give into dynamics of quantum phase transitions.

cond-mat.stat-mech↗
arXiv2005

Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity in a Quantum Universe

We study the role of the information deposited in the environment of an open quantum system in course of the decoherence process. Redundant spreading of information -- the fact that some observables of the system can be independently ``read-off'' from many distinct fragments of the environment -- is investigated as the key to effective objectivity, the essential ingredient of ``classical reality''. This focus on the environment as a communication channel through which observers learn about physical systems underscores importance of quantum Darwinism -- selective proliferation of information about ``the fittest states'' chosen by the dynamics of decoherence at the expense of their superpositions -- as redundancy imposes the existence of preferred observables. We demonstrate that the only observables that can leave multiple imprints in the environment are the familiar pointer observables singled out by environment-induced superselection (einselection) for their predictability. Many independent observers monitoring the environment will therefore agree on properties of the system as they can only learn about preferred observables. In this operational sense, the selective spreading of information leads to appearance of an objective ``classical reality'' from within quantum substrate.

quant-ph↗
arXiv2005

Predictability sieve, pointer states, and the classicality of quantum trajectories

We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection (einselection) are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states -- the most predictable states of an open quantum system selected by the predictability sieve -- are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, predictability sieve does not select well defined pointer states.)

quant-ph↗