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Register a new userSuppressing defect production during passage through a quantum critical point
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We show that a closed quantum system driven through a quantum critical point with two rates $omega_1$ (which controls its proximity to the quantum critical point) and $omega_2$ (which controls the dispersion of the low-energy quasiparticles at the critical point) exhibits novel scaling laws for defect density $n$ and residual energy $Q$. We demonstrate suppression of both $n$ and $Q$ with increasing $omega_2$ leading to an alternate route to achieving near-adiabaticity in a finite time for a quantum system during its passage through a critical point. We provide an exact solution for such dynamics with linear drive protocols applied to a class of integrable models, supplement this solution with scaling arguments applicable to generic many-body Hamiltonians, and discuss specific models and experimental systems where our theory may be tested.
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We show that the defect density $n$, for a slow non-linear power-law quench with a rate $tau^{-1}$ and an exponent $alpha>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ u$ and $z$, scales as $n sim tau^{-alpha u d/ (alpha z u+1)}$ [$n sim (alpha g^{(alpha-1)/alpha}/tau)^{ u d/(z u+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0 e 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($alpha=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.
We study defect production in a quantum system subjected to a nonlinear power law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work [D. Sen, K. Sengupta, S. Mondal, prl 101, 016806 (2008)] and present a detailed analysis of the scaling of the defect density $n$ with the quench rate $tau$ and exponent $al$ for each of the above-mentioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent $al$. We discuss several experimental systems where these theoretical predictions can be tested.
Recent advances in experimental techniques allow one to create a quantum point contact between two Fermi superfluids in cold atomic gases with a tunable transmission coefficient. In this Letter we propose that three distinct behaviors of charge transports between two Fermi superfluids can be realized in this single setup, which are the multiple Andreev reflection, the self-trapping and the Josephson oscillation. We investigate the dynamics of atom number difference between two reservoirs for different initial conditions and different transmission coefficients, and present a coherent picture of how the crossover between different regimes takes place. Our results can now be directly verified in current experimental system.
In this work we study the particle conductance of a strongly interacting Fermi gas through a quantum point contact. With an atom-molecule two-channel model, we compute the contribution to particle conductance by both the fermionic atoms and the bosonic molecules using the Keldysh formalism. Focusing on the regime above the Fermi superfluid transition temperature, we find that the fermionic contribution to the conductance is reduced by interaction compared with the quantized value for the non-interacting case; while the bosonic contribution to the conductance exhibits a plateau with non-universal values that is larger than the quantized conductance. This feature is particularly profound at temperature close to the superfluid transition. We emphasize that the enhanced conductance arises because of the bosonic nature of closed channel molecules and the low-dimensionality of the quantum point contact.
We study the thermodynamics of the relativistic quantum O($N$) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form $P(T)=P(0)+N(T^3/c^2)calF_N(Delta/T)$ where $c$ is the velocity of the excitations at the QCP and $Delta$ is a characteristic zero-temperature energy scale. Using both a large-$N$ approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function $calF_N$. For small values of $N$ ($Nlesssim 10$) we find that $calF_N(x)$ is nonmonotonous in the quantum critical regime ($|x|lesssim 1$) with a maximum near $x=0$. The large-$N$ approach -- if properly interpreted -- is a good approximation both in the renormalized classical ($xlesssim -1$) and quantum disordered ($xgtrsim 1$) regimes, but fails to describe the nonmonotonous behavior of $calF_N$ in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio $Tkt/rho_s(0)$ is very close to $pi/2$, implying that the stiffness $rho_s(Tkt^-)$ at the transition is only slightly reduced with respect to the zero-temperature stiffness $rho_s(0)$. Finally, we briefly discuss the experimental determination of the universal function $calF_2$ from the pressure of a Bose gas in an optical lattice near the superfluid--Mott-insulator transition.
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