ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 08 Sep 2024 19:40:39 GMT2024-09-08T19:40:39Z50191- Quantitative conditions do not guarantee the validity of the adiabatic approximationhttps://scholarbank.nus.edu.sg/handle/10635/53120Title: Quantitative conditions do not guarantee the validity of the adiabatic approximation
Authors: Tong, D.M.; Singh, K.; Kwek, L.C.; Oh, C.H.
Abstract: In this Letter, we point out that the widely used quantitative conditions in the adiabatic theorem are insufficient in that they do not guarantee the validity of the adiabatic approximation. We also reexamine the inconsistency issue raised by Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.160408] and elucidate the underlying cause. © 2005 The American Physical Society.
Fri, 09 Sep 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531202005-09-09T00:00:00Z
- Sufficiency criterion for the validity of the adiabatic approximationhttps://scholarbank.nus.edu.sg/handle/10635/53198Title: Sufficiency criterion for the validity of the adiabatic approximation
Authors: Tong, D.M.; Singh, K.; Kwek, L.C.; Oh, C.H.
Abstract: We examine the quantitative condition which has been widely used as a criterion for the adiabatic approximation but was recently found insufficient. Our results indicate that the usual quantitative condition is sufficient for a special class of quantum mechanical systems. For general systems, it may not be sufficient, but it, along with additional conditions, is sufficient. The usual quantitative condition and the additional conditions constitute a general criterion for the validity of the adiabatic approximation, which is applicable to all N-dimensional quantum systems. Moreover, we illustrate the use of the general quantitative criterion in some physical models. © 2007 The American Physical Society.
Mon, 09 Apr 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531982007-04-09T00:00:00Z
- A note on the geometric phase in adiabatic approximationhttps://scholarbank.nus.edu.sg/handle/10635/52756Title: A note on the geometric phase in adiabatic approximation
Authors: Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
Abstract: The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough. © 2005 Elsevier B.V. All rights reserved.
Mon, 23 May 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/527562005-05-23T00:00:00Z
- Adiabatic approximation in open systems: An alternative approachhttps://scholarbank.nus.edu.sg/handle/10635/95729Title: Adiabatic approximation in open systems: An alternative approach
Authors: Yi, X.X.; Tong, D.M.; Kwek, L.C.; Oh, C.H.
Abstract: The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system composed of the open system and ancilla, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation as well as the relation to the other definition are established and discussed. A high-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin- particle in time-dependent magnetic fields is analysed. © 2007 IOP Publishing Ltd.
Sun, 21 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/957292007-01-21T00:00:00Z
- The hybrid quantum computerhttps://scholarbank.nus.edu.sg/handle/10635/98280Title: The hybrid quantum computer
Authors: Kwek, L.C.; Lim, Y.L.; Wu, C.; Chen, J.-L.; Liu, X.; Feng, X.; Tong, D.M.; Choo, K.W.; Oh, C.H.
Abstract: In this paper, we look at the possibility of realizing one-way quantum computing through a hybrid quantum computing architecture based on stationary qubits inside an optical cavity and flying qubits (photons). It has been shown that direct qubit-qubit interactions for two-qubit gate implementations can be replaced by the experimentally less demanding generation of single photons on demand and linear optics photon pair measurements. The outcomes of these measurements indicate either the completion of the gate or the presence of the original qubits, such that the operation can be repeated until success. © 2007 MAIK "Nauka/Interperiodica".
Wed, 01 Aug 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/982802007-08-01T00:00:00Z
- Geometric phases for nondegenerate and degenerate mixed stateshttps://scholarbank.nus.edu.sg/handle/10635/52963Title: Geometric phases for nondegenerate and degenerate mixed states
Authors: Singh, K.; Tong, D.M.; Basu, K.; Chen, J.L.; Du, J.F.
Abstract: The issue of phase holonomy of both nondegenerate and degenerate mixed state undergoing unitary evolution was considered. Starting with the nondegenerate case, it was shown that the usual procedure of subtracting the dynamical phase from the total phase to yield the geometric phase, does not hold for mixed states. To this end, an expression for the geometric phase that was gauge invariant was furnished.
Sat, 01 Mar 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/529632003-03-01T00:00:00Z
- Geometric phase for mixed stateshttps://scholarbank.nus.edu.sg/handle/10635/114336Title: Geometric phase for mixed states
Authors: Kwek, L.C.; Tong, D.M.; Chen, J.L.; Du, J.F.; Choo, K.W.; Ravishankar, R.; Kaszlikowski, D.; Oh, C.H.
Abstract: We present a kinematic approach for obtaining the geometric phase of a mixed state under nonunitary evolution. This phase is gauge-invariant and measurable and leads to well-known results for unitary evolution. © Nauka/Interperiodica 2006.
Wed, 01 Feb 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1143362006-02-01T00:00:00Z
- Geometric phase for mixed stateshttps://scholarbank.nus.edu.sg/handle/10635/114335Title: Geometric phase for mixed states
Authors: Tong, D.-M.; Chen, J.-L.; Du, J.-F.
Abstract: The geometric phase of mixed states with non-degenerate eigenvalues is investigated. A general formula of geometric phase for mixed state under unitary evolution is given. In particular, we also furnish an expression of Hamiltonians for equivalent evolutions, by which one can understand what kind of evolutional operator U(t) (or Hamiltonian) is related to zero instantaneous dynamic phase. Moreover, the geometric phase and related Hamiltonians in the spin-half case are provided as an explicit example.
Sun, 01 Jun 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1143352003-06-01T00:00:00Z
- Geometric phase of Dicke state of excitons in N coupled quantum dotshttps://scholarbank.nus.edu.sg/handle/10635/96719Title: Geometric phase of Dicke state of excitons in N coupled quantum dots
Authors: Tong, D.M.; Kwek, L.C.; Couteau, C.; Oh, C.H.
Abstract: We investigate the nature of geometric phases generated by the evolution of the superposition of Dicke states of excitons in N coupled quantum dots. Based on a sequence of laser pulses, arbitrary superposition of the Dicke states of excitons can be generated. By properly choosing the superposition and using the controllable laser pulses, geometric phase with any expected value can be realized. The main advantage of using coupled quantum dots is that one uses a collective behavior, rather than addressing individually qubits, for instance, like with trapped ions configuration, which require a heavy setup in order to perform a gate. © World Scientific Publishing Company.
Mon, 20 Dec 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/967192004-12-20T00:00:00Z
- General formalism of Hamiltonians for realizing a prescribed evolution of a qubithttps://scholarbank.nus.edu.sg/handle/10635/96700Title: General formalism of Hamiltonians for realizing a prescribed evolution of a qubit
Authors: Tong, D.M.; Chen, J.-L.; Kwek, L.C.; Lai, C.H.; Oh, C.H.
Abstract: The inverse problem for the evolution of a qubit was investigated. A general formalism was proposed to establish the Hamiltonian for a qubit system that is required to evolve along a particular path. Both the unitary and nonunitary evolutions of mixed states of a qubit system were detailed.
Mon, 01 Dec 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/967002003-12-01T00:00:00Z
- Geometric phase for entangled states of two spin-1/2 particles in rotating magnetic fieldhttps://scholarbank.nus.edu.sg/handle/10635/96716Title: Geometric phase for entangled states of two spin-1/2 particles in rotating magnetic field
Authors: Tong, D.M.; Kwek, L.C.; Oh, C.H.
Abstract: The geometric phase for states of two spin-1/2 particles in rotating magnetic field is calculated, in particular, the noncyclic and cyclic non-adiabatic phases for the general case are explicitly derived and discussed. We find that the cyclic geometric phase for the entangled state can always be written as a sum of the phases of the two particles respectively; the same cannot be said for the noncyclic phase. We also investigate the geometric phase of mixed state of one particle in a biparticle system, and we find that the geometric phase for one subsystem of an entangled system is always affected by another subsystem of the entangled system.
Fri, 31 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/967162003-01-31T00:00:00Z
- Geometric phase in open systems: Beyond the Markov approximation and weak-coupling limithttps://scholarbank.nus.edu.sg/handle/10635/96717Title: Geometric phase in open systems: Beyond the Markov approximation and weak-coupling limit
Authors: Yi, X.X.; Tong, D.M.; Wang, L.C.; Kwek, L.C.; Oh, C.H.
Abstract: Beyond the quantum Markov approximation and the weak-coupling limit, we present a general theory to calculate the geometric phase for open systems with and without conserved energy. As an example, the geometric phase for a two-level system coupling both dephasingly and dissipatively to its environment is calculated. Comparison with the results from quantum trajectory analysis is presented and discussed. © 2006 The American Physical Society.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/967172006-01-01T00:00:00Z
- Operator-sum representation of time-dependent density operators and its applicationshttps://scholarbank.nus.edu.sg/handle/10635/97435Title: Operator-sum representation of time-dependent density operators and its applications
Authors: Tong, D.M.; Kwek, L.C.; Oh, C.H.; Chen, J.-L.; Ma, L.
Abstract: An arbitrary time-dependent density operator of an open system was described in terms of an operator-sum representation. Its initial condition and the path of its evolution in the state space were ignored. A general expression of Kraus operators for arbitrary time-dependent density operator was obtained. The significance of the results was proved through several examples.
Sat, 01 May 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/974352004-05-01T00:00:00Z
- Relation between geometric phases of entangled bipartite systems and their subsystemshttps://scholarbank.nus.edu.sg/handle/10635/99018Title: Relation between geometric phases of entangled bipartite systems and their subsystems
Authors: Tong, D.M.; Sjöqvist, E.; Kwek, L.C.; Oh, C.H.; Ericsson, M.
Abstract: Geometric phases of entangled states of bipartite systems under bilocal unitary evolution and of the mixed states of their subsystems were discussed. It was found that the cyclic geometric phase for entangled states with nondegenerate eigenvalues under bilocal unitary evolution can always be decomposed into a sum of weighted non-modular pure state phases. The results showed that the mixed state geometric phase of one subsystem is generally different from that of the entangled state even if the other subsystem is kept fixed.
Fri, 01 Aug 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/990182003-08-01T00:00:00Z
- Kinematic approach to the mixed state geometric phase in nonunitary evolutionhttps://scholarbank.nus.edu.sg/handle/10635/97020Title: Kinematic approach to the mixed state geometric phase in nonunitary evolution
Authors: Tong, D.M.; Sjöqvist, E.; Kwek, L.C.; Oh, C.H.
Abstract: A kinematic approach to the mixed state geometric phase in nonunitary evolution was proposed. The proposed geometric phase was shown to be gauge invariant, depending only upon the path the state space of the considered system. It was demonstrated that the proposed phase for nonunitarily evolving mixed states was testable experimentally in interferometry. The phase was also shown to lead to the previously obtained results when the evolution is unitary.
Fri, 20 Aug 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/970202004-08-20T00:00:00Z
- Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed stateshttps://scholarbank.nus.edu.sg/handle/10635/97019Title: Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states
Authors: Tong, D.M.; Sjöqvist, E.; Filipp, S.; Kwek, L.C.; Oh, C.H.
Abstract: Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed-state concept proposed in [Phys. Rev. Lett. 90, 050403 (2003)] to degenerate density operators. The first- and second-order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states. ©2005 The American Physical Society.
Tue, 01 Mar 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/970192005-03-01T00:00:00Z
- Kraus representation for the density operator of a qubithttps://scholarbank.nus.edu.sg/handle/10635/97027Title: Kraus representation for the density operator of a qubit
Authors: Tong, D.M.; Chen, J.L.; Huang, J.Y.; Kwek, L.C.; Oh, C.H.
Abstract: We show that the time evolution of the density operator of a qubit can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems. © Nauka/Interperiodica 2006.
Wed, 01 Nov 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/970272006-11-01T00:00:00Z
- Quantum nonlocality of Heisenberg XX model with site-dependent coupling strengthhttps://scholarbank.nus.edu.sg/handle/10635/97697Title: Quantum nonlocality of Heisenberg XX model with site-dependent coupling strength
Authors: Wu, C.; Chen, J.-L.; Tong, D.M.; Kwek, L.C.; Oh, C.H.
Abstract: We show that the generalized Bell inequality is violated in the extended Heisenberg model when the temperature is below a threshold value. The threshold temperature values are obtained by constructing exact solutions of the model using the temperature-dependent correlation functions. The effect due to the presence of an external magnetic field is also illustrated.
Fri, 26 Nov 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/976972004-11-26T00:00:00Z
- Field-induced meniscus dynamics and its impact on the nanoscale tip-surface interfacehttps://scholarbank.nus.edu.sg/handle/10635/117348Title: Field-induced meniscus dynamics and its impact on the nanoscale tip-surface interface
Authors: Xie, X.N.; Chung, H.J.; Tong, D.M.; Sow, C.H.; Wee, A.T.S.
Abstract: We describe the spatiotemporal evolution of the nanoscale tip-surface junction during field-induced water meniscus formation in the junction. The motion of the meniscus and tip was analyzed on the basis of typical parameters concerning the nanoscale meniscus and tip-surface configuration. Being attracted by the electric field, the meniscus generates a repulsive hydrodynamic impact force counteracting the electrostatic force on the tip. The imbalance of the forces leads to an increase of the tip-surface separation distance, and the increase is related to the initial experimental parameters including tip bias voltage and tip spring constant. An explicit equation was derived for the estimation of the tip-surface junction enlargement effect. The theoretical results were confirmed by atomic force microscope (AFM) in situ observations of tip repulsion under electric fields. The induced tip-surface junction enlargement has significant implications in AFM nanolithography, e.g., it could facilitate the formation of nanostructures with high vertical dimensions/aspect ratios. © 2007 American Institute of Physics.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1173482007-01-01T00:00:00Z