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Jacek Dziarmaga

Publications and source records attributed to Jacek Dziarmaga.

At least 91 records · Page 5Linked to original sources
arXiv2008

Dynamics of a quantum phase transition with decoherence: the quantum Ising chain in a static spin environment

We consider a linear quench from the paramagnetic to ferromagnetic phase in the quantum Ising chain interacting with a static spin environment. Both decoherence from the environment and non-adiabaticity of the evolution near a critical point excite the system from the final ferromagnetic ground state. For weak decoherence and relatively fast quenches the excitation energy, proportional to the number of kinks in the final state, decays like an inverse square root of a quench time, but slow transitions or strong decoherence make it decay in a much slower logarithmic way. We also find that fidelity between the final ferromagnetic ground state and a final state after a quench decays exponentially with a size of a chain, with a decay rate proportional to average density of excited kinks, and a proportionality factor evolving from 1.3 for weak decoherence and fast quenches to approximately 1 for slow transitions or strong decoherence. Simultaneously, correlations between kinks randomly distributed along the chain evolve from a near-crystalline anti-bunching to a Poissonian distribution of kinks in a number of isolated Anderson localization centers randomly scattered along the chain.

quant-ph↗
arXiv2008

Frustration, Area Law, and Interference in Quantum Spin Models

We study frustrated quantum systems from a quantum information perspective. Within this approach, we find that highly frustrated systems do not follow any general ''area law'' of block entanglement, while weakly frustrated ones have area laws similar to those of nonfrustrated systems away from criticality. To calculate the block entanglement in systems with degenerate ground states, typical in frustrated systems, we define a ''cooling'' procedure of the ground state manifold, and propose a frustration degree and a method to quantify constructive and destructive interference effects of entanglement.

quant-ph↗
arXiv2008

Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model

We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising model on the $8\times8$ square lattice are found to be very accurate even with the smallest non-trivial truncation parameter.

cond-mat.other↗
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↗
arXiv2007

Quantum phase transition in the one-dimensional compass model

We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions $σ_i^zσ_{i+1}^z$ and $σ_i^xσ_{i+1}^x$, alternating between even/odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest neighbor pseudospin correlations change discontinuosly and indicate divergent correlation length at the first order quantum phase transition. At this transition one finds the disordered ground state of the compass model with high degeneracy $2\times 2^{N/2}$ in the limit of $N\to\infty$.

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

Dynamics of a quantum phase transition in the random Ising model

A quantum phase transition from paramagnetic to ferromagnetic phase is driven by a time-dependent external magnetic field. For any rate of the transition the evolution is non-adiabatic and finite density of defects is excited in the ferromagnetic state. The density of excitations has only logarithmic dependence on the transition rate. This is much weaker than any usual power law scaling predicted for pure systems by the Kibble-Zurek mechanism.

cond-mat.dis-nn↗
arXiv2005

Images of a Bose-Einstein condensate in position and momentum space

In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state which is dynamical Bogoliubov vacuum. The dynamical vacuum has a simple diagonal form in a time-dependent orthonormal basis of single particle modes. This diagonal representation leads to a gaussian probability distribution for possible outcomes of density measurements in position and momentum space. In these notes we also discuss relations with the U(1) symmetry breaking version of the Bogoliubov theory and give two equivalent gaussian integral representations of the dynamical vacuum state.

cond-mat.other↗
arXiv2005

Dynamics of quantum phase transition: exact solution in quantum Ising model

Quantum Ising model is an exactly solvable model of quantum phase transition. This paper gives an exact solution when the system is driven through the critical point at finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with probability depending on the transition rate. Average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.

cond-mat.other↗
arXiv2005

N-particle Bogoliubov vacuum state

We consider the Bogoliubov vacuum state in the number-conserving Bogoliubov theory proposed by Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We show that in the particle representation the vacuum can be written in a simple diagonal form. The vacuum state can describe the stationary N-particle ground state of a condensate in a trap, but it can also represent a dynamical state when, for example, a Bose-Einstein condensate initially prepared in the stationary ground state is subject to a time-dependent perturbation. In both cases the diagonal form of the Bogoliubov vacuum can be obtained by basically diagonalizing the reduced single particle density matrix of the vacuum. We compare N-body states obtained within the Bogoliubov theory with the exact ground states in a 3-site Bose-Hubbard model. In this example, the Bogoliubov theory fails to accurately describe the stationary ground state in the limit when N goes to infinity but a small fraction of depleted particles is kept constant.

cond-mat.other↗
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↗
arXiv2005

Images of a Bose-Einstein condensate at finite temperature

A condensate initially prepared at finite temperature evolves under external time-dependent perturbation into a time-dependent mixed state. In these notes I use number-conserving time-dependent Bogoliubov theory to derive probability distribution for different outcomes of density measurement on the time-dependent excited state.

cond-mat.mes-hall↗
arXiv2005

Images of a Bose-Einstein condensate: diagonal dynamical Bogoliubov vacuum

Evolution of a Bose-Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent Bogoliubov theory: a condensate initially in its ground state Bogoliubov vacuum evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is tailored for simulations of quantum measurements on an excited condensate. As an example we work out phase imprinting of a dark soliton followed by a density measurement.

cond-mat.mes-hall↗
arXiv2004

Laser cooling all the way down to Fermi superfluid

Numerical simulations for realistic experimental parameters demonstrate that laser cooling on the attractive side of the Feshbach resonance can drive fermions much below the superfluid transition. For the assumed set of experimental parameters the transition takes place at $0.35T_F$, and laser cooling can drive the system down to at least $0.085T_F$ in a time of a few seconds. Superfluid growth is self-consistently included in simulations.

cond-mat.other↗
arXiv2004

Quantum fluctuations of a vortex in a dilute Bose-Einstein condensate

A vortex in a quasi two-dimensional Bose-Einstein condensate is subject to the Magnus force and can be effectively described as a planar particle in a uniform magnetic field. Quantization of this effective particle leads to the lowest Landau level where the most localized wave function is a gaussian. In this gaussian state vortex position seems to fluctuate with an average magnitude set by the magnetic width of the gaussian. We readdress this problem using the number-conserving version of the Bogoliubov theory. We find that the Bogoliubov mode that might be interpreted as a fluctuation of vortex position actually does not contribute to position fluctuation at all. The only non-zero contribution comes from phonons but it is an order of magnitude less than the simple estimate, based on the magnetic width of the effective gaussian wave packet.

cond-mat.other↗
arXiv2004

Fast partial decoherence of a superconducting flux qubit in a spin bath

The superconducting flux qubit has two quantum states with opposite magnetic flux. Environment of nuclear spins can find out the direction of the magnetic flux after a decoherence time $τ_0$ inversely proportional to the magnitude of the flux and the square root of the number of spins. When the Hamiltonian of the qubit drives fast coherent Rabi oscillations between the states with opposite flux, then flux direction is flipped at a constant rate $ω$ and the decoherence time $τ=ωτ_0^2$ is much longer than $τ_0$. However, on closer inspection decoherence actually takes place on two timescales. The long time $τ$ is a time of full decoherence but a part of quantum coherence is lost already after the short time $τ_0$. This fast partial decoherence biases coherent flux oscillations towards the initial flux direction and it can affect performance of the superconducting devices as qubits.

cond-mat.other↗
arXiv2004

Conditional quantum dynamics with several observers

We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the density matrices each observer ascribes to the system under the Markov approximation, and show that this problem can be reduced to the case of a single "super-observer", who has access to all the acquired data. The key problem - consistency of the sets of data acquired by different observers - is then reduced to the probability that a given combination of data sets will be ever detected by the "super-observer". The resulting conditional master equations are applied to several physical examples: homodyne detection of phonons in quantum Brownian motion, photo-detection and homodyne detection of resonance fluorescence from a two-level atom. We introduce {\it relative purity} to quantify the correlations between the information about the system gathered by different observers from their measurements of the environment. We find that observers gain the most information about the state of the system and they agree the most about it when they measure the environment observables with eigenstates most closely correlated with the optimally predictable {\it pointer basis} of the system.

quant-ph↗