Physics of negative absolute temperatures

Resolving the Debate between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures

Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs' volume entropy. Both entropies have shortcomings─while Boltzmann entropy predicts unphysical negative/infinite absolute temperatures for small systems with an unbounded energy spectrum, Gibbs entropy entirely disallows negative absolute temperatures, in disagreement with experiments. We consider a relative energy window, motivated by the Heisenberg energy-time uncertainty principle and eigenstate thermalization in quantum mechanics. The proposed entropy ensures positive, finite temperatures for systems without a maximum limit on their energy and allows negative absolute temperatures in bounded energy spectrum systems, e.g., with population inversion. It also closely matches canonical ensemble predictions for prototypical systems, thus correctly describing the zero-point energy of an isolated quantum harmonic oscillator. Overall, we enable accurate thermodynamic models for isolated systems with few degrees of freedom.

Cooling with fermionic thermal reservoirs

The quantum reservoirs commonly considered in open-quantum systems theory are those modeled by quantum harmonic oscillators, which are called bosonic reservoirs. Recently, quantum reservoirs modeled by two-level systems, the so-called fermionic reservoirs, have received attention due to their features. Given that the components of these reservoirs have a finite number of energy levels, unlike bosonic reservoirs, some studies are being carried out to explore the advantages of using this type of reservoir, especially in the operation of heat machines. In this paper, we carry out a case study of a quantum refrigerator operating in the presence of bosonic or fermionic thermal reservoirs, and we show that fermionic baths have advantages over bosonic ones.

Observation of Light Thermalization to Negative-Temperature Rayleigh-Jeans Equilibrium States in Multimode Optical Fibers

Although the temperature of a thermodynamic system is usually believed to be a positive quantity, under particular conditions, negative-temperature equilibrium states are also possible. Negative-temperature equilibriums have been observed with spin systems, cold atoms in optical lattices, and two-dimensional quantum superfluids. Here we report the observation of Rayleigh-Jeans thermalization of light waves to negative-temperature equilibrium states. The optical wave relaxes to the equilibrium state through its propagation in a multimode optical fiber-i.e., in a conservative Hamiltonian system. The bounded energy spectrum of the optical fiber enables negative-temperature equilibriums with high energy levels (high-order fiber modes) more populated than low energy levels (low-order modes). Our experiments show that negative-temperature speckle beams are featured, in average, by a nonmonotonic radial intensity profile. The experimental results are in quantitative agreement with the Rayleigh-Jeans theory without free parameters. Bringing negative temperatures to the field of optics opens the door to the investigation of fundamental issues of negative-temperature states in a flexible experimental environment.

Droplet to soliton crossover at negative temperature in presence of bi-periodic optical lattices

It is shown that the phenomenon of negative temperature essentially occurs in Bose-Einstein condensate due to the realization of the upper bound energy state utilizing a combination of expulsive harmonic oscillator and optical lattice potentials. We study the existence of quantum droplets at negative temperature and droplet-to-soliton crossover in the binary Bose-Einstein condensate mixture in the presence of bi-periodic optical lattices and expulsive-BOL confinements. Based on the beyond mean field approximation, we employ the extended Gross-Pitäevskii equation and calculate the exact analytical form of wavefunction solutions for BOL, expulsive-BOL confinements. An interesting transition of quantum droplets from positive to negative temperatures and the droplet-to-soliton crossover by modulating the disorder in BOL potential are illustrated. The affirmation of such crossover is performed by exploring the profile of atomic condensate density which smoothly transits from being a flat top density in optical lattice confinement to a bright soliton for BOL trap. Further, we confirm the crossover by exploring the energy per particle and the variation in the root mean square size of the condensate with respect to the potential depth of the BOL trap. Eventually, all of this aid us to construct a phase diagram in a space between the amplitude of BOL potential depth and particle number which reveals the formation of droplet and soliton phases. In expulsive-BOL confinement, it is seen that the impact of the expulsive trap is insignificant on atomic condensate density in the droplet phase and it becomes prominent in the soliton region. Further, the variation of total energy reveals that the amplitude of the expulsive oscillator strengthens the droplet phase and leads to an increase in the negative temperature of the considered system.

Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach

We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behavior on a shorter timescale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation.

Fermi's Golden Rule for Spontaneous Emission in Absorptive and Amplifying Media

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.

Exact Analytical Model for Bose-Einstein Condensate at Negative Temperature

We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap introduces asymmetry and the corresponding temporal dynamics reveal atom distillation at negative temperature.

Efficiencies and Work Losses for Cycles Interacting with Reservoirs of Apparent Negative Temperatures

Inverted quantum states of apparent negative temperature store the work required for their creation [Struchtrup. Phys. Rev. Lett. 2018, 120, 250602]. Thermodynamic cycles operating between a classical reservoir and an inverted state reservoir seem to have thermal efficiencies at or even above unity. These high efficiencies result from inappropriate definition adopted from classical heat engines. A properly defined efficiency compares the work produced in the cycle to the work expended in creating the reservoir. Due to work loss to irreversible processes, this work storage based efficiency always has values below unity.

Efficiency of a Quantum Otto Heat Engine Operating under a Reservoir at Effective Negative Temperatures

We perform an experiment in which a quantum heat engine works under two reservoirs, one at a positive spin temperature and the other at an effective negative spin temperature, i.e., when the spin system presents population inversion. We show that the efficiency of this engine can be greater than that when both reservoirs are at positive temperatures. We also demonstrate the counterintuitive result that the Otto efficiency can be beaten only when the quantum engine is operating in the finite-time mode.

Work Storage in States of Apparent Negative Thermodynamic Temperature

Inverted quantum states provide a challenge to classical thermodynamics, since they appear to contradict the classical formulation of the second law of thermodynamics. Ramsey interpreted these states as stable equilibrium states of negative thermodynamic temperature, and added a provision to allow these states to the Kelvin-Planck statement of the second law [N. F. Ramsey, Phys. Rev. 103, 20 (1956)PHRVAO0031-899X10.1103/PhysRev.103.20]. Since then, Ramsey's interpretation has prevailed in the literature. Here, we present an alternative option to accommodate inverted states within thermodynamics, which strictly enforces the original Kelvin-Planck statement of the second law, and reconciles inverted states and the second law by interpreting the former as unstable states, for which no temperature-positive or negative-can be defined. Specifically, we recognize inverted quantum states as temperature-unstable states, for which all processes are in agreement with the original Kelvin-Planck statement of the second law, and positive thermodynamic temperatures in stable equilibrium states. These temperature-unstable states can only be created by work done to the system, which is stored as energy in the unstable states, and can be released as work again, just as in a battery or a spring.

Relaxation to Negative Temperatures in Double Domain Systems

The engineering of quantum systems and their environments has led to our ability now to design composite or complex systems with the properties one desires. In fact, this allows us to couple two or more distinct systems to the same environment where potentially unusual behavior and dynamics can be exhibited. In this Letter we investigate the relaxation of two giant spins or collective spin ensembles individually coupled to the same reservoir. We find that, depending on the configuration of the two individual spin ensembles, the steady state of the composite system does not necessarily reach the ground state of the individual systems, unlike what one would expect for independent environments. Further, when the size of one individual spin ensemble is much larger than the second, collective relaxation can drive the second system to an excited steady state even when it starts in the ground state; that is, the second spin ensemble relaxes towards a negative-temperature steady state.

Realization of ground state in artificial kagome spin ice via topological defect-driven magnetic writing

Arrays of non-interacting nanomagnets are widespread in data storage and processing. As current technologies approach fundamental limits on size and thermal stability, enhancing functionality through embracing the strong interactions present at high array densities becomes attractive. In this respect, artificial spin ices are geometrically frustrated magnetic metamaterials that offer vast untapped potential due to their unique microstate landscapes, with intriguing prospects in applications from reconfigurable logic to magnonic devices or hardware neural networks. However, progress in such systems is impeded by the inability to access more than a fraction of the total microstate space. Here, we demonstrate that topological defect-driven magnetic writing-a scanning probe technique-provides access to all of the possible microstates in artificial spin ices and related arrays of nanomagnets. We create previously elusive configurations such as the spin-crystal ground state of artificial kagome dipolar spin ices and high-energy, low-entropy 'monopole-chain' states that exhibit negative effective temperatures.