Zenith Grant Awardee
Ville Maisi, Lund University; Klaus Ensslin, ETH Zürich; Christopher Jarzynski, University of Maryland
Information-to-work conversion from classical to quantum – a nanoscale electronic demon in double quantum dots.
When the sun hits the earth, it warms the atmosphere. The atmosphere consists of gas molecules that move the faster, the hotter the atmosphere is. Imagine it would be possible, to slow down these molecules, i.e. extract their kinetic energy, and use it to drive an electric motor. This procedure would serve two purposes, namely to cool the atmosphere and to produce electric energy. Overall energy would be conserved. In physics there is a law called the second law of thermodynamics. This law states, that the above described procedure will not work. In order to cool the atmosphere, the extracted heat would have to be at least partially transported to another reservoir, for example the earth. So cooling always comes together with heating, for macroscopic systems this can not be changed.
For an individual gas molecule it is very well possible that it slows down, for example by hitting a soft barrier. This effect, however, is compensated by other gas molecules being accelerated so that the overall systems follows the second law of thermodynamics.
Technology has advanced to a point that the velocity of individual molecules can be monitored. Similarly, for small transistors realized in semiconductors, the transport of individual electrons, the carriers of charge leading to a measurable current, can be measured. If two transistors are close to each other one can tell whether an electron is in the right, the left or none of the transistors. This information, namely where the electron is located, can be used. Furthermore, the transistors can be externally manipulated through locally applied voltages or electric fields such that the location of an electron is determined by the potential landscape and the local fluctuations, which are always present for a system at finite temperature.
In modern physics we understand that information about a system and energy that one can extract from the system are related. We can thus build a system, for example consisting of two closely positioned transistors, which we can manipulate in a way that the electrons flow in the “wrong” direction, driven by the local thermal fluctuations. This requires that we know, i.e. have the information, where the electron is and how barriers have to be shaped in order for the electron to move against the applied voltage. We can thus use information to produce an electric current.
Knowing where an electron is, is a classical concept. Quantum mechanics tells us that if we know the location of a quantum object, we can not know in principle how fast it is. In this proposal we put all of these concepts together, namely quantum mechanics, information theory, thermodynamics and semiconductor technology. Our goal is to measure a current that is driven in a system, of which we have information which is used to manipulate critical components of the system. We will put information to work.
The idea that information about microscopic fluctuations can be exploited to generate useful work has its roots in the nineteenth-century thought experiment of Maxwell’s demon. We propose to implement this idea in a nanoscale, solid-state electronic system designed to permit us to measure directly the flow of electric current generated by the “demon”, and to study the conversion of information to work across the transition from classical to quantum behavior.
The experimental platform we propose consists of a pair of quantum dots (QD’s) – small semiconducting structures that confine electrons. Each dot is coupled to an electron reservoir through barriers with a tunable height. In the classical regime, the occupation state of each dot, 0 or 1, represents one bit of information that can be monitored continuously. By manipulating the QD energy levels εL and εR in response to the observed occupation states of the dots, we will produce a current of electrons flowing one by one against an imposed electric bias eV = μR – μL. These results will provide the first demonstration of using information alone to produce electrical work against an external voltage bias. Moreover, the work will be measured directly, by observation of the current generated, rather than inferred indirectly from the dynamics of the system state.
By tuning system parameters to achieve rapid rates of tunneling between the dots, we will access the quantum regime in which the QD energy levels hybridize to form a bonding (ground) and anti-bonding (excited) state. In each of these states the electron is in a quantum superposition between the left and right dots, rather than in a classical state in which it occupies either one dot or the other. By enhancing the rate of charge detection, and by employing microwave spectroscopy techniques both to measure and to control the superposition states, we will be able to probe information-to-work conversion in this quantum regime.
These experiments will be supported by state-of-the art theory. We will develop models that accurately describe charge transport and work production in both the classical and quantum regimes, carefully accounting for unavoidable features such as back-tunneling, measurement errors, finite detector bandwidth and system noise sources. We will additionally draw upon our experience with fluctuation theorems and thermodynamic uncertainty relations to develop novel theories to describe the transition from classical to quantum non-equilibrium behavior, an under-explored area in nanoscale information thermodynamics.
Our experiments will establish QD’s as an ideal platform for studying information as fuel, they will demonstrate landmark proofs of principle, and – in combination with our theoretical efforts – they will contribute profoundly to our understanding of information thermodynamics in both classical and quantum nanoscale systems.