We develop a theory of damping of low-energy, collective excitations in a quasi-two-dimensional, homogenous, dipolar Bose gas at zero temperature, via processes whereby an excitation decays into two excitations with lower energy. We find that owing to the nature of the low-energy spectrum of a quasi-two-dimensional dipolar gas, such processes cannot occur unless the momentum of the incoming quasiparticle exceeds a critical value ${\mathbf{k}}_{\text{crit}}$ . We find that as the dipolar interaction strength is increased, this critical value shifts to larger momenta. Our predictions can be directly verified in current experiments on dipolar Bose condensates using Bragg spectroscopy, and provide valuable insight into the quantum many-body physics of dipolar gases.We develop a theory of damping of low-energy, collective excitations in a quasi-two-dimensional, homogenous, dipolar Bose gas at zero temperature, via processes whereby an excitation decays into two excitations with lower energy. We find that owing to the nature of the low-energy spectrum of a quasi-two-dimensional dipolar gas, such processes cannot occur unless the momentum of the incoming quasiparticle exceeds a critical value ${\mathbf{k}}_{\text{crit}}$. We find that as the dipolar interaction strength is increased, this critical value shifts to larger momenta. Our predictions can be directly verified in current experiments on dipolar Bose condensates using Bragg spectroscopy, and provide valuable insight into the quantum many-body physics of dipolar gases.

arXiv:1307.2910Physical Review ASep 25, 201318 citations

Quantum field theory for the chiral clock transition in one spatial dimension

Seth Whitsitt, Rhine Samajdar, Subir Sachdev A

We describe the quantum phase transition in the $N$ -state chiral clock model in spatial dimension $d=1$ . With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$ , the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_{N}$ symmetry, to a gapped phase with the ${\mathbb{Z}}_{N}$ symmetry restored. The transition has dynamical critical exponent $z\ensuremath{\ne}1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$ , involving the onset of a single-boson condensate in the background of a higher-dimensional $N$ -boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2\ensuremath{-}d$, with $4\ensuremath{-}N$ chosen to be of order $2\ensuremath{-}d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$ , finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\ensuremath{\nu}$.We describe the quantum phase transition in the $N$-state chiral clock model in spatial dimension $d=1$. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_{N}$ symmetry, to a gapped phase with the ${\mathbb{Z}}_{N}$ symmetry restored. The transition has dynamical critical exponent $z\ensuremath{\ne}1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single-boson condensate in the background of a higher-dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2\ensuremath{-}d$, with $4\ensuremath{-}N$ chosen to be of order $2\ensuremath{-}d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\ensuremath{\nu}$.

arXiv:1808.07056Physical review. B./Physical review. BNov 9, 201881 citations

Renormalization group theory of critical dynamics in bose systems

Fumihiko Tanaka

Jan 1, 19760 citations

The trapped two-dimensional Bose gas: from Bose–Einstein condensation to Berezinskii–Kosterlitz–Thouless physics

Zoran Hadzibabic, P. Krüger, Marc Cheneau +2 more

We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.

arXiv:0712.1265New Journal of PhysicsApr 30, 2008111 citations

{\mathbf{k}}_{\text{crit}}

. We find that as the dipolar interaction strength is increased, this critical value shifts to larger momenta. Our predictions can be directly verified in current experiments on dipolar Bose condensates using Bragg spectroscopy, and provide valuable insight into the quantum many-body physics of dipolar gases.

We describe the quantum phase transition in the

N

-state chiral clock model in spatial dimension

d=1

. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and

N=3

, the clock model is expected to have a direct phase transition from a gapped phase with a broken global

{\mathbb{Z}}_{N}

symmetry, to a gapped phase with the

{\mathbb{Z}}_{N}

symmetry restored. The transition has dynamical critical exponent $z\ensuremath{\ne}1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in

d=1

, involving the onset of a single-boson condensate in the background of a higher-dimensional

N

-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2\ensuremath{-}d$, with $4\ensuremath{-}N$ chosen to be of order $2\ensuremath{-}d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for

N=3

, finding good evidence for a direct phase transition, and obtain estimates for

z

and the correlation length exponent $\ensuremath{\nu}$.