Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonance... more Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.
In recent years, bright soliton-like structures composed of gaseous Bose-Einstein conden-sates ha... more In recent years, bright soliton-like structures composed of gaseous Bose-Einstein conden-sates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solu-tions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on eluci-dating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Fina...
New Developments on Fundamental Problems in Quantum Physics, 1997
We describe how to manipulate, and characterize the motional state of a trapped ion. We also give... more We describe how to manipulate, and characterize the motional state of a trapped ion. We also give a method to measure an arbitrary motional observable in a single shot.
Atomtronics is an emerging field of quantum technology dealing with matter-wave circuits of ultra... more Atomtronics is an emerging field of quantum technology dealing with matter-wave circuits of ultra-cold atoms manipulated in magnetic or laser-generated guides of different shapes and intensity. Atomtronic circuits are promised to define quantum networks of new types in which coherent fluids can be feasibly controlled with the know how of the atomic and molecular physics quantum technology. This way, atomtronics can provide the basis for new quantum devices with enhanced precision, control and flexibility. At the same time, new quantum simulators and emulators harnessing coherent current flows can be defined. Here, we survey the atomtronics-enabled quantum technology and we draw a roadmap on the field for the years to come. The latest progress achieved in matter-wave circuits design and atom-chips are reviewed. Atomtronic networks have been used as platforms to study many-body physics in a new way, both at equilibrium and at non-equilibrium. Relevant problems in mesoscopic physics, l...
We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible ... more We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra-and inter-species interactions. We derive analytically a universal equation for the density around the different boundaries in one, two and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas-Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas-Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.
For two states of opposite parity that cross as a function of an external magnetic field, the add... more For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a conical intersection as a function of external spatial coordinates. We consider the effect of the resulting geometric phase for ultracold polar molecules. For a Bose-Einstein condensate in the mean-field approximation, the geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.
We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta... more We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated. We show how to directly measure the sensitivity of the ion motion to small variations in the external parameters.
We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein co... more We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including 'ball and shell' formations and axially/radially separated states, with a marked sensitivity to the potential perturbations and the relative atom number in each species. Incorporation of linear trap perturbations, albeit weak, are found to be essential to match the range of equilibrium density profiles observed in a recent 87 Rb-133 Cs BoseEinstein condensate experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)]. Our analysis of this experiment demonstrates that sensitivity to linear trap perturbations is likely to be important factor in interpreting the results of similar experiments in the future.
Under certain conditions, the quantum δ-kicked harmonic oscillator displays quantum resonances. W... more Under certain conditions, the quantum δ-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the δ-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.
This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation ... more This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation (GPE). As proposals for interferometry and creating nonlocal quantum superpositions have been formed, it has become necessary to investigate effects not present in mean-field models. We investigate the effect of harmonic confinement on the internal degrees of freedom, as the ratio of zero-point harmonic oscillator length to classical soliton length, for different numbers of atoms. We derive a first-order energy correction for the addition of a harmonic potential to the many-body wave function and use this to create a variational technique based on energy minimization of this wave function for an arbitrary number of atoms, and include numerics based on diagonalization of the Hamiltonian in a basis of harmonic oscillator Fock states. Finally we compare agreement between a Hartree product ground state and the Bethe ansatz solution with a Gaussian envelope localizing the center of mass and show a region of good agreement.
This paper presents intuitive interpretations of tightly focused beams of light by drawing analog... more This paper presents intuitive interpretations of tightly focused beams of light by drawing analogies to two-dimensional electrostatics, magnetostatics and fluid dynamics. We use a Helmholtz decomposition of the transverse polarization components in the transverse plane to introduce generalized radial and azimuthal polarization states. This reveals the interplay between transverse and longitudinal polarization components in a transparent fashion. Our approach yields a comprehensive understanding of tightly focused laser beams, which we illustrate through several insightful examples.
We report observations of the formation and subsequent decay of a vortex lattice in a Bose-Einste... more We report observations of the formation and subsequent decay of a vortex lattice in a Bose-Einstein condensate confined in a hybrid optical-magnetic trap. Vortices are induced by rotating the anharmonic magnetic potential that provides confinement in the horizontal plane. We present simple numerical techniques based on image analysis to detect vortices and analyze their distributions. We use these methods to quantify the amount of order present in the vortex distribution as it transitions from a disordered array to the energetically favorable ordered lattice.
We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is s... more We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. To demonstrate the power law behavior explicitly we consider the evolutions of the second- and fourth-order momentum moments, and cumulants, for an initially Gaussian momentum distribution corresponding to the Maxwell-Boltzmann distribution of an ideal gas at thermal equilibrium.
Assuming the existence of a Bose-Einstein condensate composed of the majority of a sample of ultr... more Assuming the existence of a Bose-Einstein condensate composed of the majority of a sample of ultracold, trapped atoms, perturbative treatments to incorporate the non-condensate fraction are common. Here we describe how this may be carried out in an explicitly number-conserving fashion, providing a common framework for the work of various authors; we also briefly consider issues of implementation, validity and application of such methods. 1
We report the observation of quantum reflection from a narrow, attractive, potential using bright... more We report the observation of quantum reflection from a narrow, attractive, potential using bright solitary matter-waves formed from a 85 Rb Bose-Einstein condensate. We create narrow potentials using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the trapping of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a narrow Gaussian potential well; a more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.
... Received 27 June 1995 We use the theory of continuous measurement to analyze the effects of d... more ... Received 27 June 1995 We use the theory of continuous measurement to analyze the effects of decoherence on a realistic model of a quantum computer based on cavity QED. We show how decoherence affects the computation, and methods to prevent it. ...
We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quan... more We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode-locking. A hierarchy for the rational numbers known as the Farey Tree provides an ordering of the Arnol'd tongues and hence the accelerator modes. This ordering can provide a means for determining rational approximants to the Earth's gravitational acceleration.
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonance... more Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.
In recent years, bright soliton-like structures composed of gaseous Bose-Einstein conden-sates ha... more In recent years, bright soliton-like structures composed of gaseous Bose-Einstein conden-sates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solu-tions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on eluci-dating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Fina...
New Developments on Fundamental Problems in Quantum Physics, 1997
We describe how to manipulate, and characterize the motional state of a trapped ion. We also give... more We describe how to manipulate, and characterize the motional state of a trapped ion. We also give a method to measure an arbitrary motional observable in a single shot.
Atomtronics is an emerging field of quantum technology dealing with matter-wave circuits of ultra... more Atomtronics is an emerging field of quantum technology dealing with matter-wave circuits of ultra-cold atoms manipulated in magnetic or laser-generated guides of different shapes and intensity. Atomtronic circuits are promised to define quantum networks of new types in which coherent fluids can be feasibly controlled with the know how of the atomic and molecular physics quantum technology. This way, atomtronics can provide the basis for new quantum devices with enhanced precision, control and flexibility. At the same time, new quantum simulators and emulators harnessing coherent current flows can be defined. Here, we survey the atomtronics-enabled quantum technology and we draw a roadmap on the field for the years to come. The latest progress achieved in matter-wave circuits design and atom-chips are reviewed. Atomtronic networks have been used as platforms to study many-body physics in a new way, both at equilibrium and at non-equilibrium. Relevant problems in mesoscopic physics, l...
We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible ... more We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra-and inter-species interactions. We derive analytically a universal equation for the density around the different boundaries in one, two and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas-Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas-Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.
For two states of opposite parity that cross as a function of an external magnetic field, the add... more For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a conical intersection as a function of external spatial coordinates. We consider the effect of the resulting geometric phase for ultracold polar molecules. For a Bose-Einstein condensate in the mean-field approximation, the geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.
We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta... more We propose an experimental configuration, within an ion trap, by which a quantum mechanical delta-kicked harmonic oscillator could be realized, and investigated. We show how to directly measure the sensitivity of the ion motion to small variations in the external parameters.
We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein co... more We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including 'ball and shell' formations and axially/radially separated states, with a marked sensitivity to the potential perturbations and the relative atom number in each species. Incorporation of linear trap perturbations, albeit weak, are found to be essential to match the range of equilibrium density profiles observed in a recent 87 Rb-133 Cs BoseEinstein condensate experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)]. Our analysis of this experiment demonstrates that sensitivity to linear trap perturbations is likely to be important factor in interpreting the results of similar experiments in the future.
Under certain conditions, the quantum δ-kicked harmonic oscillator displays quantum resonances. W... more Under certain conditions, the quantum δ-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the δ-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.
This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation ... more This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation (GPE). As proposals for interferometry and creating nonlocal quantum superpositions have been formed, it has become necessary to investigate effects not present in mean-field models. We investigate the effect of harmonic confinement on the internal degrees of freedom, as the ratio of zero-point harmonic oscillator length to classical soliton length, for different numbers of atoms. We derive a first-order energy correction for the addition of a harmonic potential to the many-body wave function and use this to create a variational technique based on energy minimization of this wave function for an arbitrary number of atoms, and include numerics based on diagonalization of the Hamiltonian in a basis of harmonic oscillator Fock states. Finally we compare agreement between a Hartree product ground state and the Bethe ansatz solution with a Gaussian envelope localizing the center of mass and show a region of good agreement.
This paper presents intuitive interpretations of tightly focused beams of light by drawing analog... more This paper presents intuitive interpretations of tightly focused beams of light by drawing analogies to two-dimensional electrostatics, magnetostatics and fluid dynamics. We use a Helmholtz decomposition of the transverse polarization components in the transverse plane to introduce generalized radial and azimuthal polarization states. This reveals the interplay between transverse and longitudinal polarization components in a transparent fashion. Our approach yields a comprehensive understanding of tightly focused laser beams, which we illustrate through several insightful examples.
We report observations of the formation and subsequent decay of a vortex lattice in a Bose-Einste... more We report observations of the formation and subsequent decay of a vortex lattice in a Bose-Einstein condensate confined in a hybrid optical-magnetic trap. Vortices are induced by rotating the anharmonic magnetic potential that provides confinement in the horizontal plane. We present simple numerical techniques based on image analysis to detect vortices and analyze their distributions. We use these methods to quantify the amount of order present in the vortex distribution as it transitions from a disordered array to the energetically favorable ordered lattice.
We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is s... more We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. To demonstrate the power law behavior explicitly we consider the evolutions of the second- and fourth-order momentum moments, and cumulants, for an initially Gaussian momentum distribution corresponding to the Maxwell-Boltzmann distribution of an ideal gas at thermal equilibrium.
Assuming the existence of a Bose-Einstein condensate composed of the majority of a sample of ultr... more Assuming the existence of a Bose-Einstein condensate composed of the majority of a sample of ultracold, trapped atoms, perturbative treatments to incorporate the non-condensate fraction are common. Here we describe how this may be carried out in an explicitly number-conserving fashion, providing a common framework for the work of various authors; we also briefly consider issues of implementation, validity and application of such methods. 1
We report the observation of quantum reflection from a narrow, attractive, potential using bright... more We report the observation of quantum reflection from a narrow, attractive, potential using bright solitary matter-waves formed from a 85 Rb Bose-Einstein condensate. We create narrow potentials using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the trapping of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a narrow Gaussian potential well; a more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.
... Received 27 June 1995 We use the theory of continuous measurement to analyze the effects of d... more ... Received 27 June 1995 We use the theory of continuous measurement to analyze the effects of decoherence on a realistic model of a quantum computer based on cavity QED. We show how decoherence affects the computation, and methods to prevent it. ...
We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quan... more We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode-locking. A hierarchy for the rational numbers known as the Farey Tree provides an ordering of the Arnol'd tongues and hence the accelerator modes. This ordering can provide a means for determining rational approximants to the Earth's gravitational acceleration.
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Papers by S. A. Gardiner