Periodic Reporting for period 2 - Quantropy (Entropy in engineered quantum systems - Mesoscopic thermodynamics of correlated quantum states)
Reporting period: 2023-01-01 to 2024-06-30
Quantum systems that have been engineered to host correlated electronic states are of outstanding fundamental and technological interest. Often ‘exotic’ new quasi-particles emerge, such as Majorana fermions, whose inherent topological robustness forms the basis of a promising approach to quantum computation. Another recent example are sheets of pencil-lead graphene which superconduct with a proper twist between layers.
Thermodynamic probes have been central for characterising new phases of matter in bulk materials. Low-dimensional systems offer greater opportunities for control, but probing their electronic states in a similar way is notoriously difficult, in part because of the small number of electrons involved.
The objective of this project is to overcome this challenge and to develop a unique conceptual and experimental foundation for exploring correlated quantum states in low-dimensional systems by measuring thermodynamic quantities, in particular entropy. Entropy is one of the most fundamental of physical properties, and in recent years has been recognized as a key to understanding systems as diverse as qubits and black holes. Fully exploiting entropy measurements in mesoscopic physics will open up a new window to a mechanistic understanding of correlated quantum states in engineered structures, with promise for ground-breaking novel device paradigms.
Thermodynamic probes have been central for characterising new phases of matter in bulk materials. Low-dimensional systems offer greater opportunities for control, but probing their electronic states in a similar way is notoriously difficult, in part because of the small number of electrons involved.
The objective of this project is to overcome this challenge and to develop a unique conceptual and experimental foundation for exploring correlated quantum states in low-dimensional systems by measuring thermodynamic quantities, in particular entropy. Entropy is one of the most fundamental of physical properties, and in recent years has been recognized as a key to understanding systems as diverse as qubits and black holes. Fully exploiting entropy measurements in mesoscopic physics will open up a new window to a mechanistic understanding of correlated quantum states in engineered structures, with promise for ground-breaking novel device paradigms.
During the first funding period we have measured the entropy of electrons in quantum dot both in GaAs and graphene. The entropic signature of quantum states based on coherent interactions between multiple localized spins, or between a localized spin and a reservoir have been studied. Our measurements have found indications of an unexpected residual entropy for a spin localized to a quantum dot but strongly coupled to a reservoir, where the Kondo singlet should be emerging.
We pushed the theory front beyond the current experiment in a number of ways. In relation to the milestone of measuring fractional entropy in systems like the multichannel Kondo effect, we translated the conductance data into entropy, thus obtaining an estimate of how close this experiment is to measure the desired fractional entropy. In addition we showed that our experimental methods can allow detection of a dissipative phase transition due to the coupling to the charge sensor. We also put forward a theoretical proposal to measure the long sought topological entanglement entropy using our charge detection methods in presented quantum dots in the fractional quantum Hall regime.
The quantum statistics and scaling dimension of exotic particles rely on noise and cross-correlations measurements in a setup involving two sources emitting quasiparticle beams impinging on both sides of a central quantum point contact. With this approach, we obtained evidence of fractional quantum statistics for e/3 and e/5 quasiparticles emerging in the fractional quantum Hall regime and observed a novel, Andreev-like transport mechanism. Subsequently, we expanded this approach to include wave packets carrying a fractional charge along the edge of the integer quantum Hall regime, which are also predicted to obey fractional statistics. The on-going data analysis confirms this prediction.
We pushed the theory front beyond the current experiment in a number of ways. In relation to the milestone of measuring fractional entropy in systems like the multichannel Kondo effect, we translated the conductance data into entropy, thus obtaining an estimate of how close this experiment is to measure the desired fractional entropy. In addition we showed that our experimental methods can allow detection of a dissipative phase transition due to the coupling to the charge sensor. We also put forward a theoretical proposal to measure the long sought topological entanglement entropy using our charge detection methods in presented quantum dots in the fractional quantum Hall regime.
The quantum statistics and scaling dimension of exotic particles rely on noise and cross-correlations measurements in a setup involving two sources emitting quasiparticle beams impinging on both sides of a central quantum point contact. With this approach, we obtained evidence of fractional quantum statistics for e/3 and e/5 quasiparticles emerging in the fractional quantum Hall regime and observed a novel, Andreev-like transport mechanism. Subsequently, we expanded this approach to include wave packets carrying a fractional charge along the edge of the integer quantum Hall regime, which are also predicted to obey fractional statistics. The on-going data analysis confirms this prediction.
In GaAs quantum circuits it has become possible to measure the entropy of a double quantum dot system. This paves the way to the measurement of entanglement entropy, as outlined in our proposal. Various scnarios have been worked out theoretically. For graphene quantum circuits the entropy for single and double carrier occupation has been measured for a single quantum dot. In addition, time-resolved measurements enabled the measurement of the degeneracy of ground and excited states.