Motivated by the recent realization of the strongly correlated driven many-body system showing tunable continuous to the discontinuous quantum phase transition betweenMott insulator (MI) and superfluid with staggered phase (π-SF), we study the two-band extended Bose Hubbard model using the density matrix renormalization group with mean-field (CMFT+DMRG) method in one spatial dimension. In this model, the inter-band coupling and effective detuning energy are related to the resonant shaking frequency and amplitude. We calculate the superfluid order parameters and density of bosons in lower and upper bands to identify the underlining MI and π-SF phases. The bosons transfer from the lower band (ground state) to the upper band (first excited state) when the resonant shaking frequency is increased. For small shaking amplitude, the transfer of bosons is sudden giving rise to discontinuous MI to π-SF transition. For the case of large shaking amplitudes. the boson transferscontinuouslyreflect a continuous MI to π-SF transition. We compare our results with the earlier work.Motivated by the recent realization of the strongly correlated driven many-body system showing tunable continuous to the discontinuous quantum phase transition betweenMott insulator (MI) and superfluid with staggered phase (π-SF), we study the two-band extended Bose Hubbard model using the density matrix renormalization group with mean-field (CMFT+DMRG) method in one spatial dimension. In this model, the inter-band coupling and effective detuning energy are related to the resonant shaking frequency and amplitude. We calculate the superfluid order parameters and density of bosons in lower and upper bands to identify the underlining MI and π-SF phases. The bosons transfer from the lower band (ground state) to the upper band (first excited state) when the resonant shaking frequency is increased. For small shaking amplitude, the transfer of bosons is sudden giving rise to discontinuous MI to π-SF transition. For the case of large shaking amplitudes. the boson transferscontinuouslyreflect a continuous MI to π-SF transition. We compare our results with the earlier work.

AIP conference proceedingsJan 1, 20240 citations

Ground State

O. M. Braun, Yuri S. Kivshar

Springer eBooksJan 1, 20040 citations

Oscillating potential well in the complex plane and the adiabatic theorem

Stefano Longhi

A quantum particle in a slowly changing potential well $V(x,t)=V(x\ensuremath{-}{x}_{0}(\ensuremath{\epsilon}t))$, periodically shaken in time at a slow frequency $\ensuremath{\epsilon}$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $\ensuremath{\sim}1/\ensuremath{\epsilon}$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by ${\ensuremath{\omega}}_{0}$ and periodically shaken in a complex plane. Two different spatial displacements ${x}_{0}(t)$ are assumed: the real spatial displacement ${x}_{0}(\ensuremath{\epsilon}t)=Asin(\ensuremath{\epsilon}t)$, corresponding to ordinary Hermitian shaking, and the complex one ${x}_{0}(\ensuremath{\epsilon}t)=A\ensuremath{-}Aexp(\ensuremath{-}i\ensuremath{\epsilon}t)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $\ensuremath{\epsilon}$ is close to an odd resonance of ${\ensuremath{\omega}}_{0}$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.A quantum particle in a slowly changing potential well $V(x,t)=V(x\ensuremath{-}{x}_{0}(\ensuremath{\epsilon}t))$, periodically shaken in time at a slow frequency $\ensuremath{\epsilon}$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $\ensuremath{\sim}1/\ensuremath{\epsilon}$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by ${\ensuremath{\omega}}_{0}$ and periodically shaken in a complex plane. Two different spatial displacements ${x}_{0}(t)$ are assumed: the real spatial displacement ${x}_{0}(\ensuremath{\epsilon}t)=Asin(\ensuremath{\epsilon}t)$, corresponding to ordinary Hermitian shaking, and the complex one ${x}_{0}(\ensuremath{\epsilon}t)=A\ensuremath{-}Aexp(\ensuremath{-}i\ensuremath{\epsilon}t)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $\ensuremath{\epsilon}$ is close to an odd resonance of ${\ensuremath{\omega}}_{0}$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.

arXiv:1710.04429Physical Review AOct 2, 20177 citations

Probing Empty States

ScienceJun 9, 20000 citations

Squeezing of States

WORLD SCIENTIFIC eBooksApr 27, 20150 citations

Observation of Photon-Assisted Tunneling in Optical Lattices

Carlo Sias, Hans Lignier, Yeshpal Singh +4 more

We have observed tunneling suppression and photon-assisted tunneling of Bose-Einstein condensates in an optical lattice subjected to a constant force plus a sinusoidal shaking. For a sufficiently large constant force, the ground energy levels of the lattice are shifted out of resonance and tunneling is suppressed; when the shaking is switched on, the levels are coupled by low-frequency photons and tunneling resumes. Our results agree well with theoretical predictions and demonstrate the usefulness of optical lattices for studying solid-state phenomena.We have observed tunneling suppression and photon-assisted tunneling of Bose-Einstein condensates in an optical lattice subjected to a constant force plus a sinusoidal shaking. For a sufficiently large constant force, the ground energy levels of the lattice are shifted out of resonance and tunneling is suppressed; when the shaking is switched on, the levels are coupled by low-frequency photons and tunneling resumes. Our results agree well with theoretical predictions and demonstrate the usefulness of optical lattices for studying solid-state phenomena.

arXiv:0709.3137Physical Review LettersFeb 1, 2008240 citations

V(x)

sustaining two bound states spaced in frequency by ${\ensuremath{\omega}}_{0}$ and periodically shaken in a complex plane. Two different spatial displacements

{x}_{0}(t)

are assumed: the real spatial displacement ${x}_{0}(\ensuremath{\epsilon}t)=Asin(\ensuremath{\epsilon}t)$, corresponding to ordinary Hermitian shaking, and the complex one ${x}_{0}(\ensuremath{\epsilon}t)=A\ensuremath{-}Aexp(\ensuremath{-}i\ensuremath{\epsilon}t)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $\ensuremath{\epsilon}$ is close to an odd resonance of ${\ensuremath{\omega}}_{0}$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.