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Papers by Anna Minguzzi

Research paper thumbnail of Strongly interacting trapped one-dimensional quantum gases: Exact solution

AVS Quantum Science

Understanding the effect of correlations in interacting many-body systems is one of the main chal... more Understanding the effect of correlations in interacting many-body systems is one of the main challenges in quantum mechanics. While the general problem can only be addressed by approximate methods and numerical simulations, in some limiting cases, it is amenable to exact solutions. This Review collects the predictions coming from a family of exact solutions which allows us to obtain the many-body wavefunction of strongly correlated quantum fluids confined by a tight waveguide and subjected to any form of longitudinal confinement. It directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved. The exact solution applies to bosons, fermions, and mixtures. It allows us to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillation ...

Research paper thumbnail of Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

Physical Review A, 2009

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic... more We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a non-interacting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions and behaviour of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large bosonfermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as Cp −4 at large momenta, like in the case of a pure bosonic TG gas. The coefficient C is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions "fermionize" under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

Research paper thumbnail of Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

The European Physical Journal Special Topics, 2017

We study Tan's contact, i.e. the coefficient of the highmomentum tails of the momentum distributi... more We study Tan's contact, i.e. the coefficient of the highmomentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion.Our results are relevant for ongoing experiments with ultracold atomic gases.

Research paper thumbnail of Dimensional crossover in a Fermi gas and a cross-dimensional Tomonaga-Luttinger model

Physical Review A, 2016

We describe the dimensional crossover in a noninteracting Fermi gas in an anisotropic trap, obtai... more We describe the dimensional crossover in a noninteracting Fermi gas in an anisotropic trap, obtained by populating various transverse modes of the trap. We study the dynamical structure factor and drag force. Starting from a dimension d, the (d + 1)-dimensional case is obtained to a good approximation with relatively few modes. We show that the dynamical structure factor of a gas in a d-dimensional harmonic trap simulates an effective 2d-dimensional box trap. We focus then on the experimentally relevant situation when only a portion of the gas in harmonic confinement is probed and give a condition to obtain the behavior of a d-dimensional gas in a box. Finally, we propose a generalized Tomonaga-Luttinger model for the multimode configuration and compare the dynamical structure factor in the 2D limit with the exact result, finding that it is accurate in the backscattering region and at low energy.

Research paper thumbnail of Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

Physical Review A, 2015

We consider an interacting, one-dimensional Bose gas confined in a split trap, obtained by an har... more We consider an interacting, one-dimensional Bose gas confined in a split trap, obtained by an harmonic potential with a localized barrier at its center. We address its quantum-transport properties through the study of dipolar oscillations, which are induced by a sudden quench of the position of the center of the trap. We find that the dipole-mode frequency strongly depends on the interaction strength between the particles, yielding information on the classical screening of the barrier and on its renormalization due to quantum fluctuations. Furthermore, we predict a parity effect which becomes most prominent in the strongly correlated regime.

Research paper thumbnail of Dynamic structure factor and drag force in a one-dimensional strongly interacting Bose gas at finite temperature

Physical Review A, 2015

We study the effect of thermal and quantum fluctuations on the dynamical response of a onedimensi... more We study the effect of thermal and quantum fluctuations on the dynamical response of a onedimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeauimpenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.

Research paper thumbnail of High-momentum tail in the Tonks gas under harmonic confinement

Physics Letters A, 2002

We use boson-fermion mapping to show that the single-particle momentum distribution in a one-dime... more We use boson-fermion mapping to show that the single-particle momentum distribution in a one-dimensional gas of hard point-like bosons (Tonks gas) inside a harmonic trap decays as p −4 at large momentum p. The relevant integrals expressing the one-body density matrix are evaluated for small numbers of particles in a simple Monte Carlo approach to test the extent of the asymptotic law and to illustrate the slow decay of correlations between the matter-wave field at different points.

Research paper thumbnail of Quantum fluctuations of a Bose-Josephson junction in a quasi-one-dimensional ring trap

Physical Review A, 2009

Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction,... more Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long range order can be experimentally probed in principle using an interference measurement. The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting 1D fluid. We also evaluate the particle density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction of the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.

Research paper thumbnail of Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

Physical Review Letters, 2014

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subject... more We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U (1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.

Research paper thumbnail of Shell structure in the density profiles for noninteracting fermions in anisotropic harmonic confinement

Physical Review A, 2003

We develop a Green's function method to evaluate the exact equilibrium particle-density profiles ... more We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of large number of particles, we find that for very anisotropic traps the quantum effects due to singlelevel occupancy and the deviations from the Thomas-Fermi approximation are visible also for mesoscopic clouds.

Research paper thumbnail of Strongly interacting trapped one-dimensional quantum gases: Exact solution

AVS Quantum Science

Understanding the effect of correlations in interacting many-body systems is one of the main chal... more Understanding the effect of correlations in interacting many-body systems is one of the main challenges in quantum mechanics. While the general problem can only be addressed by approximate methods and numerical simulations, in some limiting cases, it is amenable to exact solutions. This Review collects the predictions coming from a family of exact solutions which allows us to obtain the many-body wavefunction of strongly correlated quantum fluids confined by a tight waveguide and subjected to any form of longitudinal confinement. It directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved. The exact solution applies to bosons, fermions, and mixtures. It allows us to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillation ...

Research paper thumbnail of Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

Physical Review A, 2009

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic... more We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a non-interacting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions and behaviour of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large bosonfermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as Cp −4 at large momenta, like in the case of a pure bosonic TG gas. The coefficient C is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions "fermionize" under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

Research paper thumbnail of Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

The European Physical Journal Special Topics, 2017

We study Tan's contact, i.e. the coefficient of the highmomentum tails of the momentum distributi... more We study Tan's contact, i.e. the coefficient of the highmomentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion.Our results are relevant for ongoing experiments with ultracold atomic gases.

Research paper thumbnail of Dimensional crossover in a Fermi gas and a cross-dimensional Tomonaga-Luttinger model

Physical Review A, 2016

We describe the dimensional crossover in a noninteracting Fermi gas in an anisotropic trap, obtai... more We describe the dimensional crossover in a noninteracting Fermi gas in an anisotropic trap, obtained by populating various transverse modes of the trap. We study the dynamical structure factor and drag force. Starting from a dimension d, the (d + 1)-dimensional case is obtained to a good approximation with relatively few modes. We show that the dynamical structure factor of a gas in a d-dimensional harmonic trap simulates an effective 2d-dimensional box trap. We focus then on the experimentally relevant situation when only a portion of the gas in harmonic confinement is probed and give a condition to obtain the behavior of a d-dimensional gas in a box. Finally, we propose a generalized Tomonaga-Luttinger model for the multimode configuration and compare the dynamical structure factor in the 2D limit with the exact result, finding that it is accurate in the backscattering region and at low energy.

Research paper thumbnail of Dipole mode of a strongly correlated one-dimensional Bose gas in a split trap: Parity effect and barrier renormalization

Physical Review A, 2015

We consider an interacting, one-dimensional Bose gas confined in a split trap, obtained by an har... more We consider an interacting, one-dimensional Bose gas confined in a split trap, obtained by an harmonic potential with a localized barrier at its center. We address its quantum-transport properties through the study of dipolar oscillations, which are induced by a sudden quench of the position of the center of the trap. We find that the dipole-mode frequency strongly depends on the interaction strength between the particles, yielding information on the classical screening of the barrier and on its renormalization due to quantum fluctuations. Furthermore, we predict a parity effect which becomes most prominent in the strongly correlated regime.

Research paper thumbnail of Dynamic structure factor and drag force in a one-dimensional strongly interacting Bose gas at finite temperature

Physical Review A, 2015

We study the effect of thermal and quantum fluctuations on the dynamical response of a onedimensi... more We study the effect of thermal and quantum fluctuations on the dynamical response of a onedimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeauimpenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.

Research paper thumbnail of High-momentum tail in the Tonks gas under harmonic confinement

Physics Letters A, 2002

We use boson-fermion mapping to show that the single-particle momentum distribution in a one-dime... more We use boson-fermion mapping to show that the single-particle momentum distribution in a one-dimensional gas of hard point-like bosons (Tonks gas) inside a harmonic trap decays as p −4 at large momentum p. The relevant integrals expressing the one-body density matrix are evaluated for small numbers of particles in a simple Monte Carlo approach to test the extent of the asymptotic law and to illustrate the slow decay of correlations between the matter-wave field at different points.

Research paper thumbnail of Quantum fluctuations of a Bose-Josephson junction in a quasi-one-dimensional ring trap

Physical Review A, 2009

Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction,... more Using a Luttinger-liquid approach we study the quantum fluctuations of a Bose-Josephson junction, consisting of a Bose gas confined to a quasi one-dimensional ring trap which contains a localized repulsive potential barrier. For an infinite barrier we study the one-particle and two-particle static correlation functions. For the one-body density-matrix we obtain different power-law decays depending on the location of the probe points with respect to the position of the barrier. This quasi-long range order can be experimentally probed in principle using an interference measurement. The corresponding momentum distribution at small momenta is also shown to be affected by the presence of the barrier and to display the universal power-law behavior expected for an interacting 1D fluid. We also evaluate the particle density profile, and by comparing with the exact results in the Tonks-Girardeau limit we fix the nonuniversal parameters of the Luttinger-liquid theory. Once the parameters are determined from one-body properties, we evaluate the density-density correlation function, finding a remarkable agreement between the Luttinger liquid predictions and the exact result in the Tonks-Girardeau limit, even at the length scale of the Friedel-like oscillations which characterize the behavior of the density-density correlation function at intermediate distance. Finally, for a large but finite barrier we use the one-body correlation function to estimate the effect of quantum fluctuations on the renormalization of the barrier height, finding a reduction of the effective Josephson coupling energy, which depends on the length of the ring and on the interaction strength.

Research paper thumbnail of Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field

Physical Review Letters, 2014

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subject... more We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U (1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.

Research paper thumbnail of Shell structure in the density profiles for noninteracting fermions in anisotropic harmonic confinement

Physical Review A, 2003

We develop a Green's function method to evaluate the exact equilibrium particle-density profiles ... more We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of large number of particles, we find that for very anisotropic traps the quantum effects due to singlelevel occupancy and the deviations from the Thomas-Fermi approximation are visible also for mesoscopic clouds.