Abstract
We derive, from first principles and using the Weyl–Wigner formalism, a fully quantum kinetic model describing the dynamics in phase space of Dirac electrons in single-layer graphene. In the ...limit
ℏ
→ 0, we recover the well-known semiclassical Boltzmann equation, widely used in graphene plasmonics. The polarizability function is calculated and, as a benchmark, we retrieve the result based on the random-phase approximation. By keeping all orders in
ℏ
, we use the newly derived kinetic equation to construct a fluid model for macroscopic variables written in the pseudospin space. As we show, the novel
ℏ
-dependent terms can be written as corrections to the average current and pressure tensor. Upon linearization of the fluid equations, we obtain a quantum correction to the plasmon dispersion relation, of order
ℏ
2
, akin to the Bohm term of quantum plasmas. In addition, the average variables provide a way to examine the value of the effective hydrodynamic mass of the carriers. For the latter, we find a relation in which Drude’s mass is multiplied by the square of a velocity-dependent, Lorentz-like factor, with the speed of light replaced by the Fermi velocity, a feature stemming from the quasi-relativistic nature of the Dirac fermions.
Sympathetic laser cooling of a single mode graphene membrane coupled to an atomic cloud interacting via Casimir-Polder forces has been recently proposed. Here, we extend this study to the effect of ...secondary graphene membrane whose frequency may be far or close to resonance. We show that if the two mechanical modes are close together, it is possible to simultaneously cool both modes. Conversely, if the two frequencies are set far apart, the secondary mode does not affect the cooling of the first one. We also study the entanglement properties of the steady-state using the logarithmic negativity. We show how stationary mechanical entanglement between two graphene sheets can be generated by means of vacuum fluctuations. Moreover, we find that, within feasible experimental parameters, large steady-state acoustomechanical entanglement, i.e. entanglement between the phononic and mechanical mode, E N 5 , can be generated.
We propose experimentally feasible means for nondestructive thermometry of homogeneous Bose-Einstein condensates in different spatial dimensions (d∈{1,2,3}). Our impurity-based protocol suggests that ...the fundamental error bound on thermometry at the subnanokelvin domain depends highly on the dimension, in that the higher the dimension the better the precision. Furthermore, suboptimal thermometry of the condensates by using measurements that are experimentally feasible is explored. We specifically focus on measuring position and momentum of the impurity that belong to the family of Gaussian measurements. We show that, generally, experimentally feasible measurements are far from optimal, except in one dimension, where position measurements are indeed optimal. This makes realistic experiments perform very well at few nanokelvin temperatures for all dimensions, and at subnanokelvin temperatures in the one-dimensional scenario. These results take a significant step towards experimental realization of probe-based quantum thermometry of Bose-Einstein condensates, as it deals with them in one, two, and three dimensions and uses feasible measurements applicable in current experimental setups.
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