Michal Kolář

Quantum bath refrigeration towards absolute zero: challenging the unattainability principle.

A minimal model of a quantum refrigerator (QR), i.e. a periodically phase-flipped two-level system permanently coupled to a finite-capacity bath (cold bath) and an infinite heat dump (hot bath), is introduced and used to investigate the cooling of the cold bath towards the absolute zero (T = 0). Remarkably, the temperature scaling of the cold-bath cooling rate reveals that it does not vanish as T → 0 for certain realistic quantized baths, e.g. phonons in strongly disordered media (fractons) or quantized spin-waves in ferromagnets (magnons). This result challenges Nernst’s thirdlaw formulation known as the unattainability principle.

Path–phase duality with intraparticle translational–internal entanglement

The aim of this paper is to revisit the implications of complementarity when we inject into a Mach Zehnder interferometer particles with internal structure, prepared in special translational–internal entangled (TIE) intraparticle states. This correlation causes the path distinguishability to be interferometric phase-dependent in contrast to the standard case, where distinguishability depends on some external parameters (not interferometric phase). We show that such a TIE state permits us to detect small phase shifts along with almost perfect path distinguishability, beyond the constraints imposed by complementarity on simultaneous which-way and which-phase measurements for cases when distinguishability is uncoupled to interferometric phase.

Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity

We propose a scheme for spin-squeezing in the orbital motion of a Bose-Einstein condensate (BEC) in a toroidal trap. A circular lattice couples two counter-rotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include one-axis twisting and the two-axis counter-twisting which are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.

Optomechanical oscillator controlled by variation in its heat bath temperature

We propose a generation of a low-noise state of optomechanical oscillator by a temperature dependent force. We analyze the situation in which a quantum optomechanical oscillator (denoted as the membrane) is driven by an external force (produced by the piston). Both systems are embedded in a common heat bath at certain temperature T . The driving force the piston exerts on the membrane is bath temperature dependent. Initially, for T = T0, the piston is linearly coupled to the membrane. The bath temperature is then reversibly changed to T 6= T0. The change of temperature shifts the membrane, but simultaneously also increases its fluctuations. The resulting equilibrium state of the membrane is analyzed from the point of view of mechanical, as well as of thermodynamic characteristics. We compare these characteristics of membrane and derive their intimate connection. Next, we cool down the thermal noise of the membrane, bringing it out of equilibrium, still being in the contact with heat bath. This cooling retains the effective canonical Gibbs state with the effective temperature T . In such case we study the analogs of the equilibrium quantities for low-noise mechanical states of the membrane.

BETTING ON INTERFEROMETRIC PATHS AND PHASES USING TRANSLATIONAL-INTERNAL ENTANGLEMENT: THE GREEDY KING GAME

The behavior of translationally–internally entangled (TIE) states in an interferometer of the Mach–Zehnder type is studied, by means of a game whose results show that TIE states allow near-certain guessing of both path (corpuscular) and phase (wavelike) features, as opposed to conventional states that are constrained by standard complementarity.

Extracting work from quantum states of radiation

Quantum optomechanics opens a possibility to mediate a physical connection of quantum optics and classical thermodynamics. We propose and theoretically analyze a one-way chain starting from various quantum states of radiation. In the chain, the radiation state is first ideally swapped to sufficiently large mechanical oscillator (membrane). Then the membrane mechanically pushes a classical almost mass-less piston, which is pressing a gas in a small container. As a result we observe strongly nonlinear and nonmonotonic transfer of the energy stored in classical and quantum uncertainty of radiation to mechanical work. The amount of work and even its sign depends strongly on the uncertainty of the radiation state. Our theoretical prediction would stimulate an experimental proposals for such optomechanical connection to thermodynamics.

Cheating on Complementarity and Interference by Translational --- Internal Entanglement

We show that if internal and momentum states of an interfering particle are entangled, then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with practically any precision, without the complementarity constraints of which-path detection. This holds also for multipath–multistate configurations, allowing large amounts of information to be stored in a single particle. We further show that highly complex particles (e.g., molecules or macroscopic bodies) subject to fields that couple (entangle) their internal and translational (momentum) states may undergo an irresversible randomization (diffusion), manifest by the disappearance of the interference pattern, as if they are subject to decoherence. Thus, translational-internal entanglement can give rise to anomalies in quantum wavepacket propagation.

Criticality and spin squeezing in the rotational dynamics of a Bose-Einstein condensate on a ring lattice

We examine the dynamics of circulating modes of a Bose-Einstein condensate confined in toroidal lattice. Nonlinearity due to interactions leads to criticality that separates oscillatory and self-trapped phases among counter-propagating modes which however share the same physical space. In the mean-field limit, the criticality is found to substantially enhance sensitivity to rotation of the system. Analysis of the quantum dynamics reveals the fluctuations near criticality are significant, that we explain using spin-squeezing formalism visualized on a Bloch sphere. We utilize the squeezing to propose a Ramsey interferometric scheme that suppresses fluctuation in the relevant quadrature sensitive to rotation.

FROM STATISTICAL PHYSICS METHODS TO ALGORITHMS

After a brief review of the Survey Propagation equations defined over single instances of complex glassy-like Hamiltonians, we discuss their application to the search for minimum energy configurations in difficult combinatorial optimization problems. Furthermore, we show that the application of arbitrary external field is helpful in the investigation of the topology of the configuration space.

Position and Momentum Entanglement of Dipole-Dipole Interacting Atoms in Optical Lattices

We consider a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole-dipole interactions. The Einstein-Podolsky-Rosen (EPR) “paradox” [Einstein 1935] with translational variables is then modified by lattice-diffraction effects. We study a possible mechanism of creating such diatom entangled states by varying the effective mass of the atoms.