Quantum Correlations and Temperature Fluctuations in Nanoscale Systems

This thesis addresses two different topics related to the physics of nanoscale systems. The first topic concerns quantum correlations and entanglement between electrons in solid-state systems, with a focus on how to generate electronic orbital entanglement on a sub-decoherence time scale and how to achieve experimentally more feasible entanglement detection schemes. The second topic concerns heat transport and temperature fluctuations in nanoscale systems, with a focus on how to utilize temperature fluctuations for calorimetric detection of single particles. The thesis comprises five papers.

In Paper I, we propose a quantum dot system to generate and detect, using cotunneling processes, orbitally entangled pairs of electrons on a sub-decoherence time scale.

In Paper II, we investigate, by applying an entanglement witness, the minimal number of zero-frequency current cross-correlation measurements needed to detect bipartite entanglement between two flying qubits.

In Paper III, we consider energy and temperature fluctuations, and the influence of charging effects, in a metallic island tunnel coupled to a normal metallic lead, the so-called single electron box.

In Paper IV, we investigate nanoscale quantum calorimetry and propose a setup consisting of a metallic island and a superconducting lead to realize a nanoscale calorimeter that may probe the energies of tunneling electrons.

In Paper V, we investigate photon transport statistics of a microwave cavity, including the short-time statistics of single photon emissions and the long-time statistics of heat transport through the cavity.

Over the last century, mankind has experienced an unparalleled technological revolution. This revolution has been particularly noticable in the fields of electronics and information technology, where we today take computers, mobile phones, the internet and other telecommunications for granted in our daily lives. Much of the technological development has been made possible thanks to basic research in the fields of physics and electronics during the 19th and 20th centuries, which has given us an increased understanding of fundamental phenomena such as electromagnetism as well as new inventions, such as the transistor. But as much as basic research has paved the way for new technology, the technological evolution has also paved the way for new research possibilities. Thanks to new technology, it is today possible to control and manipulate components on increasingly smaller length scales in a way that yesterday's physicists could only dream of. This allows us to explore completely new regimes with exciting, novel physics in so-called nanoscale systems, small components where the dimensions may be as small as a millionth of a millimeter.

The physics of nanoscale systems differs significantly from our daily, macroscopic world. Single particles, such as electrons and photons, typically play a crucial role for the functionality of these systems, whether it is a nanoscale transistor or a nanoscale engine. New phenomena arise that we normally do not observe in our daily lives. This includes, among other things, so-called quantum effects and the increasing importance of fluctuations and surface physics as the dimensions are scaled down. In this thesis, we treat two particular phenomena which are both present in nanosystems: quantum correlations and temperature fluctuations.

Quantum correlations are correlations that arise between particles which are quantum entangled, i.e., their states (e.g., position, momentum or spin) cannot be described independently of each other, despite full knowledge about the system as a whole. The prime example of an entangled state is the singlet state of two spins. In that case, the total spin is zero, i.e., the spins must be pointing in opposite directions. However, which spin is pointing in which direction is undefined; they are both in a quantum mechanical superposition between up and down along any arbitrary measurement axis, at least until a measurement is performed.

The presence of quantum correlations between entangled particles in quantum physics was first highlighted in the mid-1930s. Their actual existence was first questioned since they violate a fundamental physical principle called local realism in classical physics. But during the second half of the 20th century, experiments confirmed their existence and with the advent of quantum information theory during the 1980s, quantum correlations and quantum entanglement came to emerge as indispensable resources for quantum computers. Quantum computers are computers taking advantage of quantum effects to perform more efficient algorithms than classical computers. Many algorithms which are meant to be used in quantum computers are based on the access to quantum entangled particles which display quantum correlations. It is therefore a neccessity to be able to generate and detect quantum entanglement to build quantum computers.

In principle any particles may be entangled. The main problem, though, is that entanglement is a very fragile resource, that is easily lost as the entangled particles interact with other particles in their surrounding, a process called decoherence. Electrons, which would be the natural choice given their role in conventional electronics, are unfortunately particularly exposed to decoherence. The main reason is that they are charged, making them interact strongly with their environment. In this thesis, we propose a way of generating and detecting electrons on a time scale much shorter than the time scale on which the interaction with the environment destroys the entanglement. The idea is to use so-called cotunneling processes to both generate and detect the entanglement between pairs of electrons. These processes take place on the picosecond time scale, much shorter than the nanosecond time scale on which the decoherence destroys the entanglement. We also investigate how the detection of entanglement can be made simpler in nanoscale systems. Conventional methods require many complicated measurements, but it turns out that by using so-called entanglement witnesses it is actually possible to detect entanglement with much fewer measurements.

The second topic treated in this thesis concerns temperature fluctuations. Fluctuations, i.e., deviations from the mean value of a certain quantity, become more and more important as the system size of a physical system decreases. In small systems, such as nanoscale systems, it is therefore crucial to take into account the noise in, for instance, temperature and heat to describe the physics correctly. Quantum thermodynamics is the field of physics describing heat transport in small, quantum mechanical systems where those fluctuations play an important role. There are many promising applications within this field, such as heat engines which may generate electricity out of heat with high efficiencies.

In this thesis, we specifically consider the possibilities of utilizing temperature fluctuations to detect single particles, such as photons or electrons, in nanoscale systems. By coupling a superconductor to a small piece of metal, we may detect electrons that are transferred between the superconductor and the metal piece using the temperature fluctuations induced in the metal. This method, called quantum calorimetry, would, hopefully, in the future facilitate new investigations of quantum thermodynamical phenomena in nanoscale systems. A concrete example of such a phenomenon is emissions of photons from a microwave cavity, which is discussed in the fifth paper of this thesis.

Overall this thesis aims at contributing to an increasing understanding for quantum correlations and temperature fluctuations in nanoscale systems.