Janet Anders

Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere

Einstein realized that the fluctuations of a Brownian particle can be used to ascertain the properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics and leading to applications from energy harvesting to medical imaging. Here, we use heated optically levitated nanospheres to investigate the non-equilibrium properties of the gas surrounding them. Analysing the spheres Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics.

Computational power of correlations.

We study the intrinsic computational power of correlations exploited in measurement-based quantum computation. By defining a general framework, the meaning of the computational power of correlations is made precise. This leads to a notion of resource states for measurement-based classical computation. Surprisingly, the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimony-Holt problems emerge as optimal examples. Our work exposes an intriguing relationship between the violation of local realistic models and the computational power of entangled resource states.

Observing a quantum Maxwell demon at work

Significance Maxwell’s demon plays a central role in thermodynamics of quantum information, yet a full experimental characterization is still missing in the quantum regime. Here we use superconducting circuits to realize a quantum Maxwell demon in which all thermodynamic quantities can be controlled and measured. Using power detection resolved at the single microwave photon level and unprecedented tomography techniques, we directly measure the extracted work while tracking the qubit and cavity entropies and energies. We are thus able to fully characterize the demon’s memory after the work extraction and show that it takes full part in the thermodynamic process. The experiment establishes superconducting circuits as a testbed well suited to perform quantum thermodynamics experiments. In apparent contradiction to the laws of thermodynamics, Maxwell’s demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon’s memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.

Coherence and measurement in quantum thermodynamics

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

Thermodynamics of discrete quantum processes

We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnots thermal efficiency.

Thermal state entanglement in harmonic lattices

We investigate the entanglement properties of thermal states of the harmonic lattice in one, two, and three dimensions. We establish the value of the critical temperature for entanglement between neighboring sites and give physical reasons. Further sites are shown to be entangled only due to boundary effects. Other forms of entanglement are addressed in the second part of the paper by using the energy as witness of entanglement. We close with a comprehensive diagram showing the different phases of entanglement versus complete separability and propose techniques to swap and tune entanglement experimentally.

Landauer's principle in the quantum regime

We demonstrate the validity of Landauers erasure principle in the strong coupling quantum regime by treating the system-reservoir interaction in a thermodynamic way. We show that the initial coupling to the reservoir modifies both the energy and the entropy of the system, and provide explicit expressions for the latter for a damped quantum harmonic oscillator. These contributions are related to the Hamiltonian of mean force and dominate in the strong damping limit. They need therefore to be fully taken into account in any low temperature thermodynamic analysis of quantum systems.

Survival of entanglement in thermal states

We present a general sufficiency condition for the presence of multipartite entanglement in thermal states stemming from the ground-state entanglement. The condition is written in terms of the ground-state entanglement and the partition function and it gives transition temperatures below which entanglement is guaranteed to survive. It is flexible and can be easily adapted to consider entanglement for different splittings, as well as be weakened to allow easier calculations by approximations. Examples where the condition is calculated are given. These examples allow us to characterize a minimum gapping behavior for the survival of entanglement in the thermodynamic limit. Further, the same technique can be used to find noise thresholds in the generation of useful resource states for one-way quantum computing.

Entanglement at the quantum phase transition in a harmonic lattice

The entanglement properties of phase transition in a two-dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed for both finite number of particles and thermodynamical limit. We show that for the ground state at the critical value of the trapping potential, two entanglement measures, the negativity between two neighbouring sites and the block entropy for blocks of size 1, 2 and 3, change abruptly. Entanglement thus indicates quantum phase transitions in general, not only in the finite-dimensional case considered in Wu et al (2004 Phys. Rev. Lett.93250404). Finally, we consider the thermal state and compare its exact entanglement with a temperature entanglement witness introduced in Anders (2008 Phys. Rev. A 77 062102).

Detecting entanglement with a thermometer

We present a general argument showing that the temperature as well as other thermodynamical state variables can qualify as entanglement witnesses (EWs) for spatial entanglement. This holds for a variety of systems and we exemplify our ideas using a simple free non-interacting bosonic gas. We find that entanglement can exist at arbitrarily high temperatures, provided that we can probe smaller and smaller regions of space. We then discuss the relationship between the occurrence of Bose–Einstein condensation and our conditions for the presence of entanglement and compare the respective critical temperatures. We close with a short discussion of the idea of seeing entanglement as a macroscopic property in thermodynamical systems and its possible relation to phase transitions in general.