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Register a new userCritical Response of a Quantum van der Pol Oscillator
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Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator. We find the classical response survives down to one excitation quantum. At very weak drives, genuine quantum features arise, including diverging and negative susceptibilities. Further, the linear response is greatly enhanced by using a strong incoherent pump. These results are largely generic and can be probed in current experimental platforms suited for quantum sensing.
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We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Based on a stochastic interpretation different from the traditional Itos and Stratonovichs, we show the corresponding steady state distribution is the familiar Boltzmann-Gibbs type for arbitrary noise strength. The result provides a new angle for understanding processes without detailed balance and can be verified by experiments.
The equation of the Van der Pol oscillator, being characterized by a dissipative term, is non-Lagrangian. Appending an additional degree of freedom we bring the equation in the frame of action principle and thus introduce a one-way coupled system. As with the Van der Pol oscillator, the coupled system also involves only one parameter that controls the dynamics. The response system is described by a linear differential equation coupled nonlinearly to the drive system. In the linear approximation the equations of our coupled system coincide with those of the Bateman dual system (a pair of damped and anti-damped harmonic oscillators). The critical point of damped and anti-damped oscillators are stable and unstable for all physical values of the frictional coefficient $mu$. Contrarily, the critical points of the drive- (Van der Pol) and response systems depend crucially on the values of $mu$. These points are unstable for $mu > 0$ while the critical point of the drive system is stable and that of the response system is unstable for $mu < 0$. The one-way coupled system exhibits bifurcations which are different from those of the uncoupled Van der Pol oscillator. Our system is chaotic and we observe phase synchronization in the regime of dynamic chaos only for small values of $mu$.
We report on the direct measurement in real space of the effect of the van der Waals forces between individual Rydberg atoms on their external degrees of freedom. Clusters of Rydberg atoms with inter-particle distances of around 5 {mu}m are created by first generating a small number of seed excitations in a magneto-optical trap, followed by off-resonant excitation that leads to a chain of facilitated excitation events. After a variable expansion time the Rydberg atoms are field ionized, and from the arrival time distributions the size of the Rydberg cluster after expansion is calculated. Our experimental results agree well with a numerical simulation of the van der Waals explosion.
A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass $m$, confined to bounce elastically between two rigid walls where one is described by a non-linear van der Pol type oscillator while the other one is fixed, working as a re-injection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional non-linear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; (ii) the case where collisions of the particle does affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter ($c{hi}$) controlling the non-linearity of the moving wall. For large $c{hi}$, a diffusion on the velocity is observed leading us to conclude that Fermi acceleration is taking place. On the other hand for case (ii), the motion of the moving wall is affected by collisions with the particle. However due to the properties of the van der Pol oscillation, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicate organization.
We study high frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from conformal field theory allow us to fix the high frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality, and numerically via Quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high frequency optical conductivity, and the corresponding sum rule.
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