Raam Uzdin

Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures

Quantum heat engines (QHE) are thermal machines where the working substance is quantum. In the extreme case the working medium can be a single particle or a few level quantum system. The study of QHE has shown a remarkable similarity with the standard thermodynamical models, thus raising the issue what is quantum in quantum thermodynamics. Our main result is thermodynamical equivalence of all engine type in the quantum regime of small action. They have the same power, the same heat, the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature, i.e thermodynamic measurements can confirm the presence of quantum coherence in the device. The coherent work extraction mechanism enables power outputs that greatly exceed the power of stochastic (dephased) engines.

On the observability and asymmetry of adiabatic state flips generated by exceptional points

In open quantum systems where the effective Hamiltonian is not Hermitian, it is known that the adiabatic (or instantaneous) basis can be multivalued: by adiabatically transporting an eigenstate along a closed loop in the parameter space of the Hamiltonian, it is possible to end up in an eigenstate different from the initial eigenstate. This ‘adiabatic flip’ effect is an outcome of the appearance of a degeneracy known as an ‘exceptional point’ inside the loop. We show that contrary to what is expected of the transport properties of the eigenstate basis, the interplay between gain/loss and non-adiabatic couplings imposes fundamental limitations on the observability of this adiabatic flip effect.

Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon

For non-Hermitian Hamiltonians with an isolated degeneracy (‘exceptional point’), a model for cycling around loops that enclose or exclude the degeneracy is solved exactly in terms of Bessel functions. Floquet solutions, returning exactly to their initial states (up to a constant) are found, as well as exact expressions for the adiabatic multipliers when the evolving states are represented as a superposition of eigenstates of the instantaneous Hamiltonian. Adiabatically (i.e. for slow cycles), the multipliers of exponentially subdominant eigenstates can vary wildly, unlike those driven by Hermitian operators, which change little. These variations are explained as an example of the Stokes phenomenon of asymptotics. Improved (superadiabatic) approximations tame the variations of the multipliers but do not eliminate them.

Photorefractive solitons and light-induced resonance control in semiconductor CdZnTe.

We demonstrate the formation of (1+1) - and (2+1) -dimensional solitons in photorefractive CdZnTe:V, exploiting the intensity-resonant behavior of the space-charge field. We control the resonance optically, facilitating a 10-mus soliton formation times with very low optical power.

Theory of self-focusing in photorefractive InP

We present a theory of self-focusing and solitons in photorefractive InP, including the previously unexplained intensity resonance and the resonant enhancement of the space-charge field.

Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers

Various engine types are thermodynamically equivalent in the quantum limit of small “engine action”. Our previous derivation of the equivalence is restricted to Markovian heat baths and to implicit classical work repository (e.g., laser light in the semi-classical approximation). In this paper, all the components, baths, batteries, and engines, are explicitly taken into account. To neatly treat non-Markovian dynamics, we use mediating particles that function as a heat exchanger. We find that, on top of the previously observed equivalence, there is a higher degree of equivalence that cannot be achieved in the Markovian regime. Next, we focus on the quality of the battery charging process. A condition for positive energy increase and zero entropy increase (work) is given. Moreover, it is shown that, in the strong coupling regime, it is possible to super-charge a battery. With super-charging, the energy of the battery is increased while its entropy is being reduced at the same time.

Time-dependent Hamiltonians with 100% evolution speed efficiency

The evolution speed in projective Hilbert space is considered for Hermitian Hamiltonians and for non-Hermitian (NH) ones. Based on the Hilbert–Schmidt norm and the spectral norm of a Hamiltonian, resource-related upper bounds on the evolution speed are constructed. These bounds are valid also for NH Hamiltonians and they are illustrated for an optical NH Hamiltonian and for a NH PT-symmetric matrix Hamiltonian. Furthermore, the concept of quantum speed efficiency is introduced as measure of the system resources directly spent on the motion in the projective Hilbert space. A recipe for the construction of time-dependent Hamiltonians which ensure 100% speed efficiency is given. Generally these efficient Hamiltonians are NH but there is a Hermitian efficient Hamiltonian as well. Finally, the extremal case of a NH non-diagonalizable Hamiltonian with vanishing energy difference is shown to produce a 100% efficient evolution with minimal resources consumption.

The multilevel four-stroke swap engine and its environment

A multilevel four-stroke engine where the thermalization strokes are generated by unitary collisions with thermal bath particles is analyzed. Our model is solvable even when the engine operates far from thermal equilibrium and in the strong system–bath coupling. Necessary operation conditions for the heat machine to perform as an engine or a refrigerator are derived. We relate the work and efficiency of the device to local and non-local statistical properties of the baths (purity, index of coincidence, etc) and put upper bounds on these quantities. Finally, in the ultra-hot regime, we analytically optimize the work and find a striking similarity to results obtained for efficiency at maximal power of classical engines. The complete swap limit of our results holds for any fourstroke quantum Otto engine that is coupled to the baths for periods that are significantly longer than the thermal relaxation time.

Universal features in the efficiency at maximal work of hot quantum Otto engines

Classically, external power optimization over the coupling times of a heat engine to its baths leads to universal features in the efficiency. Here we study internal work optimization over the energy levels of a multilevel quantum Otto engine, and find similar universal features. It is shown that in the ultra-hot regime the efficiency is determined solely by the energy level optimization constraint, and is independent of the engines details. Constraints on the energy levels naturally appear due to physical limitations or design goals. For some constraints the results significantly differ from the classical universality.

Finding and pinpointing exceptional points of an open quantum system

An exceptional point (EP) is a point in the parameter space of an open quantum system in which the two eigenstates of the effectively non-Hermitian system coalesce and a topological effect can be observed. In this work we use the properties of the energy eigenvalues near the EP at three different points in order to find the exact EP location in the parameter space. This method does not require the two parameters of the system to be grouped as a single complex parameter, so it can easily be applied to Floquet operators. Finally, it is shown that by applying the Hellmann–Feynman theorem, the EP position can be obtained from a single point. The benefits of using the 3-point approach or the 1-point approach are discussed. These simple techniques may be of use in the search for new EPs in various physical systems. To demonstrate the utility of the method, we find an EP for an H+2 molecule driven by a monochromatic laser and for a laser-driven Gaussian potential.