Defect production due to quenching through a multicritical point

Divakaran, Uma; Mukherjee, Victor; Dutta, Amit; Sen, Diptiman

doi:10.1088/1742-5468/2009/02/p02007

Cited by 74 publications

(83 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(12) can be rewritten, apart from an additive constant, as the dynamical behavior of quantum systems: As discussed in more detail in Sec. VI, the gap closure at the critical point promotes dynamical excitations, preventing adiabatic evolutions whenever the adiabaticity condition T ≫ ∆ −1 is not fulfilled, where T is the total evolution time and ∆ the minimum spectral gap [33][34][35][36][37][38][39][40][41][42]. Following Ref.…”

Section: Lipkin-meshkov-glick Modelmentioning

confidence: 99%

Chopped random-basis quantum optimization

2011

View full text Add to dashboard Cite

In this work we describe in detail the Chopped RAndom Basis (CRAB) optimal control technique recently introduced to optimize t-DMRG simulations [1]. Here we study the efficiency of this control technique in optimizing different quantum processes and we show that in the considered cases we obtain results equivalent to those obtained via different optimal control methods while using less resources. We propose the CRAB optimization as a general and versatile optimal control technique. PACS numbers:Realizing artificial, controllable quantum systems has represented one of the most promising challenge in physics for the last thirty years [2]. On one side such systems could unveil unexplored features of Nature, when employed as universal quantum simulators [3]; on the other side this technology could be exploited to realize a new generation of extremely powerful devices, like quantum computers [4]. Along with the impressive progress marked recently in the construction of tunable quantum systems [5,6], there is a renewed and increasing interest in quantum optimal control (OC) theory, the study of the optimization techniques aimed at improving the outcome of a quantum process [2]. Indeed OC can prove to be crucial under several respects for the development of quantum devices: first, it can be generally employed to speed up a quantum process to make it less prone to decoherence or noise effects induced by the unavoidable interaction with the external environment. Second, considering a realistic experimental setup in which just few parameters are tunable or, in the most difficult situations, only partially tunable, OC can provide an answer about the optimal use of the available resources.Traditionally OC has been exploited in atomic and molecular physics [7][8][9]. More recently, with the advent of quantum information, the requirement of accurate control of quantum systems has become unavoidable to build quantum information processors [10][11][12][13][14][15][16]. However, the above mentioned methods often result in optimal driving fields that require a level of tunability incompatible with current experimental capabilities and in general, the calculation of the optimal fields requires an exact description of the system (either analytical or numerical). The field of application of these methods is severely limited also by the need to have access to huge amount of information about the system, e.g. computing gradients of the control fields, expectation values of observables as a function of time. Moreover, standard OC algorithms define a set of Euler-Lagrange equations that have to be solved to find the optimal control pulse [2], where the equation for the correction to the driving field is highly dependent on the constraints imposed on the system and on the figures of merit considered. This implies that considering different figures of merit and/or constraints on the system needs a redefinition of the corresponding Euler-Lagrange equations, hindering a straightforward adaptation of the optimization procedure to different s...

show abstract

Section: Lipkin-meshkov-glick Modelmentioning

confidence: 99%

Chopped random-basis quantum optimization

2011

View full text Add to dashboard Cite

show abstract

“…We shall now propose a general scaling scheme valid for quenching through a multicritical point as well as a critical point [31] using the LZ non-adiabatic transition probability [40,37] discussed before. We begin with a generic d-dimensional model Hamiltonian of the form (1.20) where σ ± = σ x ± iσ y , b(k) and ∆ (k) are model dependent functions, and ψ(k) denotes the fermionic operators (ψ 1 (k), ψ 2 (k)).…”

Section: Quenching Through a Multicritical Pointmentioning

confidence: 99%

“…Noting that the asymptotic form of the Hamiltonian at t → ±∞ is given by 30) we make a basis transformation to a representation in which σ x is diagonal. The Hamiltonian in (1.29) then gets modified to the form 31) where the time dependence has been shifted to the diagonal terms only. Applying the LZ transition probability formula, the probability of excitations is found to be 32) where |∆ k | 2 = |1 + cosk| 2 = (π − k) 4 /4 when expanded about k = π.…”

Section: Quenching Along a Gapless Linementioning

confidence: 99%

“…The Kibble-Zurek scaling has been verified in various exactly solvable spin models and systems of interacting bosons [4,13,16,17,11,5]; it has been generalized to quenching through a multicritical point [31], across a gapless phase [20,23], and along a gapless line [26,28], and to systems with quenched disorder [14], white noise [18], infinite-range interactions [27], and edge states [30]. Studies have also been made to estimate the defect density for quenching with a non-linear form [21], an oscillatory variation of an applied magnetic field [32] or under a reversal of the magnetic field [33].…”

Section: Introductionmentioning

confidence: 97%

“…The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Divakaran

Mukherjee

Dutta

et al. 2010

Lecture Notes in Physics

View full text Add to dashboard Cite

The exciting physics of quantum phase transitions has been explored extensively in the last few years [1,2]. The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].In this review, we concentrate on the dynamics of quantum spin chains swept across a quantum critical or multicritical point or along a gapless line by a slow (adiabatic) variation of a parameter appearing in the Hamiltonian of the system. Our aim is to find the scaling form of the density of defects (which, in our case, is the density of wrongly oriented spins) in the final state which is reached after the system is prepared in an initial ground state and then slowly quenched through a quantum critical point. The dynamics in the vicinity of a quantum critical point is necessarily non-adiabatic due to the divergence of the relaxation time of the underlying quantum system which forces the system to be infinitely sluggish; thus the system fails to respond to a change in a parameter of the Hamiltonian no matter how slow that rate of change may be! We first recall the Kibble-Zurek argument [34,35] which predicts a scaling form for the defect density following a slow quench through a quantum critical point. We assume that a parameter g of the Hamiltonian is varied in a linear fashion such that g − g c ∼ t/τ, where g = g c denotes the value of g at the quantum critical point and τ is the quenching time. Our interest is in the adiabatic limit, τ → ∞. The energy gap of the quantum Hamiltonian vanishes at the critical point as (g − g c ) νz whereas the relaxation time ξ τ , which is inverse of the gap, diverges at the critical point. It is clear that non-adiabaticity becomes important at a timet when the characteristic time scale of the quantum system (i.e., the relaxation time) is of the order of the inverse of the rate of change of the Hamiltonian; this yields

show abstract

Non-equilibrium Dynamics of Quantum Systems: Order Parameter Evolution, Defect Generation, and Qubit Transfer

Mondal

Sen

Sengupta

2010

Quantum Quenching, Annealing and Computation

View full text Add to dashboard Cite

The properties of systems near quantum critical points (QCPs) have been studied extensively in recent years [1,2]. A QCP is a point across which the symmetry of the ground state of a quantum system changes in a fundamental way; such a point can be accessed by changing some parameter, say λ , in the Hamiltonian governing the system. The change in the ground state across a QCP is mediated by quantum fluctuations. Unlike conventional thermal critical points, thermal fluctuations do not play a crucial role in such transitions. Similar to its thermal counterparts, the low energy physics near a QCP is associated with a number of critical exponents which characterize the universality class of such a transition. Amongst these exponents, the dynamical critical exponent z provides the signature of the relative scaling of space and time at the transition and has no counterpart in thermal phase transitions. The other exponent which is going to be important for the purpose of this review is the well-known correlation length exponent ν. These exponents are formally defined as follows. As we approach the critical point at λ = λ c , the correlation length diverges as ξ ∼ |λ − λ c | −ν , while the gap between the ground state and first excited state vanishes as ∆ E ∼ ξ −z ∼ |λ − λ c | zν . Exactly at the critical point λ = λ c , the energy of the low-lying excitations vanishes at some wave number k 0 as ω ∼ |k − k 0 | z . The critical exponents are independent of the details of the microscopic Hamiltonian; they depend only on a few parameters such as the dimensionality of the system and the symmetry of the order parameter. These features render the low energy equilibrium physics of a quantum system near a QCP truly universal.In contrast to this well-understood universality of the equilibrium properties of a system near a QCP, relatively few universal features are known in the nonequilibrium behavior of a quantum system. Initial studies in this field aimed at understanding the near-equilibrium finite temperature dynamics near a quantum critical

show abstract

Defect production due to quenching through a multicritical point

Cited by 74 publications

References 52 publications

Chopped random-basis quantum optimization

Chopped random-basis quantum optimization

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Non-equilibrium Dynamics of Quantum Systems: Order Parameter Evolution, Defect Generation, and Qubit Transfer

Contact Info

Product

Resources

About