Multiple Schrödinger Pictures and Dynamics in Shortcuts to Adiabaticity

Ibáñez, Sergio; Chen, Xi; Torrontegui, E.; Muga, J. G.; Ruschhaupt, A.

doi:10.1103/physrevlett.109.100403

Cited by 248 publications

(304 citation statements)

References 34 publications

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“…For convenience, when referring to a general adiabatic process, we mean both a conventional adiabatic process or its alternative version based on engineered timedependent fields, such as those processes named "shortcuts to adiabaticity" (STA) [22][23][24][25][26][27]. We order the initial eigenenergy values as…”

Section: Principle Of Minimal Work Fluctuations: Quantum Systemsmentioning

confidence: 99%

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Principle of minimal work fluctuations

Xiao

Gong

2015

Phys. Rev. E

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Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, in considering the Jarzynski equality e −βW = e −β∆F , a change in the fluctuations of e −βW may impact on how fast the statistical average of e −βW converges towards the theoretical value e −β∆F , where W is the work, β is the inverse temperature, and ∆F is free energy difference between two equilibrium states. Motivated by our previous study aiming at the suppression of work fluctuations, here we obtain a principle of minimal work fluctuations. In brief, adiabatic processes as treated in quantum and classical adiabatic theorems yield the minimal fluctuations in e −βW . In the quantum domain, if a system initially prepared at thermal equilibrium is subject to a work protocol but isolated from a bath during the time evolution, then a quantum adiabatic process without energy level crossing (or an assisted adiabatic process reaching the same final states as in a conventional adiabatic process) yields the minimal fluctuations in e −βW , where W is the quantum work defined by two energy measurements in the beginning and at the end of the process. In the classical domain where the classical work protocol is realizable by an adiabatic process, then the classical adiabatic process also yields the minimal fluctuations in e −βW . Numerical experiments based on a Landau-Zener process confirm our theory in the quantum domain, and our theory in the classical domain explains our previous numerical findings regarding the suppression of classical work fluctuations [G. Y. Xiao and J. B. Gong, Phys. Rev. E 90, 052132 (2014)].

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Section: Principle Of Minimal Work Fluctuations: Quantum Systemsmentioning

confidence: 99%

“…For a time- dependent Z(t) and a time-independent X 0 , the control field achieving STA is given by [23][24][25][26] …”

Section: Principle Of Minimal Work Fluctuations Manifested In a Lmentioning

confidence: 99%

Principle of minimal work fluctuations

Xiao

Gong

2015

Phys. Rev. E

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“…Such protocols have been discussed in systems ranging from atomic cavity QED setups [31,32] to optomechanics [34]. Remarkably, we show that our method works even in the highly constrained protocol introduced by Duan et al [32], where there is only a single time-dependent control field in the Hamiltonian.Our work represents a substantial advance over previous work using STA to accelerate adiabatic state transfer [20][21][22][23][24][25], as these works did not include a coupling to a continuum. It also differs significantly from studies ex-…”

mentioning

confidence: 75%

“…These techniques are generally referred to as "shortcuts to adiabaticity" (STA), and involve modifying control fields to suppress the net effect of non-adiabatic errors [20][21][22][23][24][25]. Recent experiments have successfully implemented versions of these strategies [26][27][28][29][30].A key drawback of the transitionless driving strategy and its higher order variants [20][21][22][23][24][25] is that they require the exact diagonalization of a time-dependent Hamiltonian, making them unwieldy for systems with many degrees of freedom. They are thus unsuitable for an important class of quantum state transfer problems, where the goal is to transfer an initial state in a localized system having discrete energy levels to a propagating state in a continuum such as a waveguide or a transmission line (see, e.g., [31][32][33]).…”

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confidence: 99%

Shortcuts to adiabaticity in the presence of a continuum: Applications to itinerant quantum state transfer

et al. 2017

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We present a method for accelerating adiabatic protocols for systems involving a coupling to a continuum, one that cancels both non-adiabatic errors as well as errors due to dissipation. We focus on applications to a generic quantum state transfer problem, where the goal is to transfer a state between a single level or mode, and a propagating temporal mode in a waveguide or transmission line. Our approach enables perfect adiabatic transfer protocols in this setup, despite a finite protocol speed and a finite waveguide coupling. Our approach even works in highly constrained settings, where there is only a single time-dependent control field available.Introduction-Adiabatic quantum evolution provides an efficient and robust way to implement a variety of important quantum operations including state transfer [1][2][3][4][5][6][7], state preparation [8][9][10][11], and even quantum logic gates [12][13][14]. While such protocols are robust against timing errors, they are necessarily slow, making them vulnerable to dissipation or fluctuations. There is thus considerable interest in finding ways to accelerate adiabatic protocols, such that fast evolution is possible without significant non-adiabatic errors [15][16][17][18][19]. These techniques are generally referred to as "shortcuts to adiabaticity" (STA), and involve modifying control fields to suppress the net effect of non-adiabatic errors [20][21][22][23][24][25]. Recent experiments have successfully implemented versions of these strategies [26][27][28][29][30].A key drawback of the transitionless driving strategy and its higher order variants [20][21][22][23][24][25] is that they require the exact diagonalization of a time-dependent Hamiltonian, making them unwieldy for systems with many degrees of freedom. They are thus unsuitable for an important class of quantum state transfer problems, where the goal is to transfer an initial state in a localized system having discrete energy levels to a propagating state in a continuum such as a waveguide or a transmission line (see, e.g., [31][32][33]).In this paper we present a general method for applying STA to the above class of problems. The method is based on first deriving an effective non-Hermitian Hamiltonian, and then constructing dressed-states and modified control sequences that suppress both non-adiabatic errors (due to finite protocol speed) and "dissipative" errors (due to the coupling to the continuum). We apply our technique to two ubiquitous quantum state transfer problems based on STIRAP (stimulated Raman adiabatic passage) [2]. Such protocols have been discussed in systems ranging from atomic cavity QED setups [31,32] to optomechanics [34]. Remarkably, we show that our method works even in the highly constrained protocol introduced by Duan et al. [32], where there is only a single time-dependent control field in the Hamiltonian.Our work represents a substantial advance over previous work using STA to accelerate adiabatic state transfer [20][21][22][23][24][25], as these works did not include a coupling to ...

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“…This means that two sets of Ioffe bars are required to physically realize this nonadiabatic control, which makes its experimental demonstration rather demanding. To overcome this difficulty, we apply the gauge transformation [22] to make the combined magnetic field (the original confining field and the CDF superposed) parallel to the original confining quadrupole field. The modest price one has to pay by this gauge transformation is to modify the time-dependence of the bias field B z (t) from a linear behavior.…”

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confidence: 99%

Fast control of topological vortex formation in Bose-Einstein condensates by counterdiabatic driving

et al. 2016

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Topological vortex formation has been known as the simplest method for vortex formation in BEC of alkali atoms. This scheme requires inversion of the bias magnetic field along the axis of the condensate, which leads to atom loss when the bias field crosses zero. In this Letter, we propose a scheme with which the atom loss is greatly suppressed by adding counter-diabatic magnetic field. A naive counter-diabatic field violates the Maxwell equations and we need to introduce an approximation to make it physically feasible. The resulting field requires an extra currents, which is experimentally challenging. Finally we solve this problem by applying a gauge transformation so that the counter-diabatic field is generated by controlling the original trap field with the additional control of the bias field.PACS numbers: 02.30. Yy, 37.90.+, 67.85.Fg, 03.75.Lm Demonstration of quantized vortices in a superfluid is a manifestation of the nonvanishing order parameter. Topological structure of vortices often reflects the manifold of the order parameter space. It is, therefore, natural to seek for the method to experimentally demonstrate formation of vortices once BEC of alkali metal atoms has been realized. Topological method of vortex formation is the simplest one compared with other proposals, where the spinor structure of the order parameter is fully utilized [1][2][3][4][5][6][7]. Although the vortex [6] and monopole [8,9] in BEC have been observed experimentally, establishment of methods to create such interesting quantum states more accurately in time much shorter than coherence time is important for further experimental study and applications.A condensate in the weak field seeking state (WFSS) is trapped in a quadrupole magnetic field in the xy-plane with a uniform bias field along the z-axis first and, subsequently, the bias field is reversed from B z to −B z adiabatically. Then a vortex with the winding number 2F is formed, were F is the quantum number of the hyperfine spin of the condensate. This theoretical proposal has been demonstrated experimentally by several groups [10][11][12][13][14][15]. A part of the condensate is lost while vortex formation takes place. This is due to the fact that the gap between the WFSS and the neutral state (NS) and the strong field seeking state (SFSS) is gradually closed near the center of the condensate during the vortex formation and the atoms in the trapping WFSS make transition to the NS and the SFSS through the Majorana flops. It is the purpose of this Letter to show that it is possible to suppress the Majorana flops so that more atoms are left in the trap when a vortex is formed. It is certainly desirable to have more atoms left in the trap since higher atomic density implies (i) easier measurement of physical quantities (ii) fighting against atom loss due to hyperfine spin changing collision and (iii) smaller vortex core size, which is advantageous for forming a vortex in an arbitrary position in the condensate [16]. Motivated by the concept of shortcuts to adiabaticity [17...

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Multiple Schrödinger Pictures and Dynamics in Shortcuts to Adiabaticity

Cited by 248 publications

References 34 publications

Principle of minimal work fluctuations

Principle of minimal work fluctuations

Shortcuts to adiabaticity in the presence of a continuum: Applications to itinerant quantum state transfer

Fast control of topological vortex formation in Bose-Einstein condensates by counterdiabatic driving

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