4/2019. “The Second Law and Beyond in Microscopic Quantum Setups.” In Thermodynamics in the Quantum Regime. Springer. Publisher's Version
The ability of the internal states of a working fluid to be in a coherent superposition is one of the basic properties of a quantum heat engine. It was recently predicted that in the regime of small engine action, this ability can enable a quantum heat engine to produce more power than any equivalent classical heat engine. It was also predicted that in the same regime, the presence of such internal coherence causes different types of quantum heat engines to become thermodynamically equivalent. Here, we use an ensemble of nitrogen vacancy centers in diamond for implementing two types of quantum heat engines, and experimentally observe both effects.
R. Uzdin and S. Rahav. 2018. “Global Passivity in Microscopic Thermodynamics.” Physical Review X, 8, Pp. 021064. Publisher's Version Abstract
The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems. (i) The Clausius inequality does not hold when the system and environment are initially correlated—a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g., in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds, we use them to detect unaccounted heat leaks and weak feedback operations (“Maxwell demons”) that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlations for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities, and more.
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Raam Uzdin, Ronnie Kosloff, Simone Gasparinetti, and Roee Ozeri. 2018. “Markovian heat sources with the smallest heat capacity.” New. J. Phys. , 20, Pp. 063030. Publisher's Version Abstract
Thermal Markovian dynamics is typically obtained by coupling a system to a sufficiently hot bath with a large heat capacity. Here we present a scheme for inducing Markovian dynamics using an arbitrarily small and cold heat bath. The scheme is based on injecting phase noise to the small bath. Markovianity emerges when the dephasing rate is larger than the system-bath coupling. Several unique signatures of small baths are studied. We discuss realizations in ion traps and superconducting qubits and show that it is possible to create an ideal setting where the system dynamics is indifferent to the internal bath dynamics.
Collective behavior, where a set of elements interact and generate effects that are beyond the reach of the individual noninteracting elements, is always of great interest in physics. Quantum collective effects that have no classical analog are even more intriguing. In this work, we show how to construct collective quantum heat machines and explore their performance boosts with respect to regular machines. Without interactions between the machines, the individual units operate in a stochastic, nonquantum manner. The construction of the collective machine becomes possible by introducing two simple quantum operations: coherence extraction and coherence injection. Together, these operations can harvest coherence from one engine and use it to boost the performance of a slightly different engine. For weakly driven engines, we show that the collective work output scales quadratically with the number of engines rather than linearly. Eventually, the boost saturates and then becomes linear. Nevertheless, even in saturation, work is still significantly boosted compared to individual operation. To study the reversibility of the collective machine, we introduce the “entropy-pollution” measure. It is shown that there is a regime where the collective machine is N times more reversible while producing N times more work, compared to the individual operation of N units. Moreover, the collective machine can even be more reversible than the most reversible unit in the collective. This high level of reversibility becomes possible due to a special symbiotic mechanism between engine pairs.
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.
R. Uzdin and R. Kosloff. 2016. “Speed limits in Liouville space for open quantum systems.” EPL, 115, Pp. 40003. Publisher's Version Abstract
One of the defining properties of an open quantum system is the variation of its purity in time. We derive speed limits on the rate of purity change for systems coupled to a Markovian environment. Our speed limits are based on Liouville space where density matrices are represented as vectors. This approach leads to speed limits that are always tighter compared to their parallel speed limits in Hilbert space. These bounds depend solely on the generators of the nonunitary dynamics and are independent of the particular state of the systems. Thus, they are perfectly suited to investigate dephasing, thermalization, and decorrelation processes of arbitrary states. We show that our speed limits can be attained and are therefore tight. As an application of our results we study dephasing of interacting spins, and the speed of classical and quantum correlation erasure in multi-particle system.
R. Uzdin, A. Levy, and R. Kosloff. 2015. “Equivalence of quantum heat machines, and quantum-thermodynamic signatures.” Physical Review X, 5, Pp. 031044. Publisher's Version Abstract
Quantum heat engines (QHE) are thermal machines where the working substance is a quantum object. 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 macroscopic thermodynamical results, thus raising the issue of what is quantum in quantum thermodynamics. Our main result is the thermodynamical equivalence of all engine types in the quantum regime of small action with respect to Planck’s constant. They have the same power, the same heat, and 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 effects in the device. We identify generic coherent and stochastic work extraction mechanisms and show that coherence enables power outputs that greatly exceed the power of stochastic (dephased) engines.
R. Uzdin and R. Kosloff. 9/12/2014. “The multilevel four-stroke swap engine and its environment.” New Journal of Physics, 16, Pp. 095003. Publisher's Version Abstract
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 four-stroke quantum Otto engine that is coupled to the baths for periods that are significantly longer than the thermal relaxation time.
R. Uzdin, L. Friedland, and O. Gat. 2014. “First-harmonic approximation in nonlinear chirped-driven oscillators.” Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 89, Pp. 012902. Publisher's Version Abstract
Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a “frequency equivalent” symmetric potential and to study the autoresonance breakdown phenomenon.
R. Uzdin. 2014. “The role of singular values in single copy entanglement manipulations and unambiguous state discrimination.” Journal of Physics A: Mathematical and Theoretical, 47, Pp. 165301. Publisher's Version Abstract
Unambiguous (non-orthogonal) state discrimination (USD) has a fundamental importance in quantum information and quantum cryptography. Various aspects of two-state and multiple-state USD are studied here using singular value decomposition of the evolution operator that describes a given state discriminating system. In particular, we relate the minimal angle between states to the ratio of the minimal and maximal singular values. This is supported by a simple geometrical picture in two-state USD. Furthermore, by studying the singular vectors population we find that the minimal angle between input vectors in multiple-state USD is always larger than the minimal angle in two-state USD in the same system. As an example we study what pure states can be probabilistically transformed into maximally entangled pure states in a given system.
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 engine's 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.
R. Uzdin, E.G. Dalla Torre, R. Kosloff, and N. Moiseyev. 2013. “Effects of an exceptional point on the dynamics of a single particle in a time-dependent harmonic trap.” Physical Review A - Atomic, Molecular, and Optical Physics, 88, Pp. 022505. Publisher's Version Abstract
The time evolution of a single particle in a harmonic trap with time-dependent frequency ω(t) has been well studied. Nevertheless, here we show that when the harmonic trap is opened (or closed) as a function of time while keeping the adiabatic parameter μ=[dω(t)/dt]/ω2(t) fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at μ=2. At this transition point, the time evolution has an exceptional point (EP) at all instants. This situation, where an EP of a time-dependent Hermitian Hamiltonian is obtained at any given time, is very different from other known cases. In the present case, we show that the order of the EP depends on the set of observables used to describe the dynamics. Our finding is relevant to the dynamics of a single ion in a magnetic, optical, or rf trap, and of diluted gases of ultracold atoms in optical traps.
R. Uzdin. 2013. “Resources needed for non-unitary quantum operations.” Journal of Physics A: Mathematical and Theoretical, 46, Pp. 145302. Publisher's Version Abstract
Non-unitary operations generated by an effective non-Hermitian Hamiltonian can be used to create quantum state manipulations which are impossible in Hermitian quantum mechanics. These operations include state preparation (or cooling) and non-orthogonal state discrimination. In this work we put a lower bound on the resources needed for the construction of some given non-unitary evolution. Passive systems are studied in detail and a general feature of such systems is derived. After interpreting our results using the singular value decomposition, several examples are studied analytically. In particular, we put a lower bound on the resources needed for non-Hermitian state preparation and non-orthogonal state discrimination.
R. Uzdin and O. Gat. 2013. “Time-energy trade-off in unambiguous-state-discrimination positive operator-valued measures.” Physical Review A - Atomic, Molecular, and Optical Physics, 88, Pp. 052327. Publisher's Version Abstract
Unambiguous-nonorthogonal-state discrimination has a fundamental importance in quantum information. Moreover, it can be used for entanglement distillation and secure communication. The discrimination is carried out by a positive operator-valued measure (POVM) generalized measurement, which is typically implemented by coupling the system to an ancilla. We find a trade-off between the needed energy resources and the evolution time needed to implement the POVM and express it in terms of an actionlike cost inequality. We find the realization that minimizes this actionlike cost and show that, in this case, the cost is determined by the maximal population transfer from the system to the ancilla. We demonstrate our findings in an example of a three-level system coupled to a laser.
R. Uzdin and N. Moiseyev. 2012. “Rapid azimuthal rotation in the Hermitian and non-Hermitian Landau-Zener problem.” Journal of Physics A: Mathematical and Theoretical, 45, Pp. 444033. Publisher's Version Abstract

In the limit of rapid passage in a time-dependent two-level system of the Landau–Zener type, the initial state undergoes a very simple yet non-trivial rotation. This effect takes place when the Hamiltonian reaches the stationary point of the system. We explain the origin of this rotation by simple means and extend it to open non-Hermitian (NH) systems where new features appear. In addition, we find that in contrast to the Hermitian case, the point at which this simple rotation takes place is not necessarily the point of minimal energy separation. Moreover, in NH Hamiltonian the stationary point may lie in the complex time plane, and then a surprisingly strong correction to the rotation angle appears. The NH aspects of this rotation can be observed in optical and quantum systems where decay rates can be controlled.

This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.

R. Uzdin and N. Moiseyev. 2012. “Scattering from a waveguide by cycling a non-Hermitian degeneracy.” Physical Review A - Atomic, Molecular, and Optical Physics, 85, Pp. 031804(R) . Publisher's Version Abstract
It has been recently shown that by varying the potential parameters in time so that a non-Hermitian degeneracy [exceptional point (EP)] is cycled, the nonadiabatic couplings have a large effect on the dynamics. This cardinal effect does not disappear even when the potential parameter are changed arbitrarily slow (“adiabatic process”). For a specific Hamiltonian this counterintuitive effect has been shown to be associated with the Stokes phenomenon. We study analytically the effects of EP cycling on the transmission and reflection of light in a waveguide with a small complex refractive index modulation. We find that in the adiabatic limit the oscillations in the transmission spectrum are sharply attenuated above a certain frequency where the EP is no longer cycled.
R. Uzdin, N. Moiseyev, U. Günther, and S. Rahav. 2012. “Time-dependent Hamiltonians with 100% evolution speed efficiency.” Journal of Physics A: Mathematical and Theoretical, 45, Pp. 415304. Publisher's Version Abstract
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 $\mathcal {PT}$-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.
R. Uzdin, N. Moiseyev, and A. Mailybaev. 2011. “On the observability and asymmetry of adiabatic state flips generated by exceptional points.” Journal of Physics A: Mathematical and Theoretical, 44, Pp. 435302. Publisher's Version Abstract
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.