Periodic Reporting for period 1 - PReB (Open quantum dynamics via Periodically Refreshed Baths)
Reporting period: 2020-05-01 to 2022-04-30
Modern day technology has enriched our daily life with extremely portable but powerful electronic devices like laptops and mobile phones. One of the key developments which made this possible has been the remarkable miniaturization of electronic circuits. Due to this miniaturization, current cutting-edge technology is on the threshold of encroaching upon length scales where quantum effects are important, requiring the advent of quantum technologies for further progress. In such nanoscale systems, dissipative effects due to the surrounding environment cannot be neglected. This has lead to the advent of noisy solid-state quantum devices on various platforms such as superconducting circuits, molecular junctions, nitrogen-vacancy (NV) centers in diamond etc. Fundamentally, such devices work by taking the system out-of-equilibrium by applying a drive, for example, a voltage bias. Such systems are termed ‘driven dissipative quantum many-body systems’. Though there has been tremendous experimental progress in this direction, theoretical tools for describing such systems have been lagging behind. This severely restricts our understanding of situations already achievable in experiments, thereby creating a bottleneck for development of quantum technology. This project takes steps towards bridging this gap.
The main result of the project is to introduce the 'Periodically Refreshed Baths' (PReB) scheme. This was initially envisioned as a numerical technique which would allow driven dissipative quantum many-body systems far beyond their present limitations. Later, we realized this as a situation possible to devise experimentally, and we analyzed the thermodynamics of the PReB scheme, discovering, what we call 'Periodically refreshed quantum thermal machines'. This required combining various state-of-the-art concepts from the theories of open quantum systems, condensed matter, statistical physics, quantum information and thermodynamics. These were then further put together with state-of-the-art tensor network based computational techniques.
The complexity of simulating dynamics of driven dissipative quantum many-body systems comes from (a) the macroscopic nature of the environments (baths), (b) the many degrees of freedom in the system, (c) the evolution of the system not depending only of the instantaneous state of the system, but on at least a finite history of the states of the system at previous times. The point (c) is called 'finite memory time'. The PReB scheme hinges on the idea that finite memory time implies that the system effectively only sees a finite part of the macroscopic baths. So by repeatedly obtaining finite-time dynamics in presence of finite-size baths one can reconstruct the full dynamics of the system (we prove this). But, simulating the finite-time dynamics with finite-size baths can still be quite difficult, the difficulty scaling exponentially with the number of degrees of freedom. This exponential growth is essentially due to exponential memory requirement. This is handled by using state-of-the-art tensor network techniques which borrow from the standard idea of data compression, like used daily in computers.
The results with this numerical technique were published in Phys. Rev B, 104, 045417 (2021). They were also presented in several conferences and invited talks across the world (including Republic of Korea, India, UK, Poland, USA).
Subsequently, we realized that the PReB scheme is not just a numerical technique. Instead, a particular driving protocol can be devised with realizes the PReB process experimentally. Intrigued by this, we explored the thermodynamics of such a process. Note that, this is very far from the regime of applicability of standard thermodynamics. So, the notion of thermodynamics had to be extended. We used a quantum information-inspired approach to thermodynamics, that has already been formulated in various previous works by other authors. This led to obtaining 'Periodically refreshed quantum thermal machines', which are quantum thermal machines, based on the PReB scheme. This connects various concepts from quantum information, thermodynamics, condensed matter, statistical physics.
These results are in arxiv:2202.05264 which is accepted for publication in Quantum.
The complexity of simulating dynamics of driven dissipative quantum many-body systems comes from (a) the macroscopic nature of the environments (baths), (b) the many degrees of freedom in the system, (c) the evolution of the system not depending only of the instantaneous state of the system, but on at least a finite history of the states of the system at previous times. The point (c) is called 'finite memory time'. The PReB scheme hinges on the idea that finite memory time implies that the system effectively only sees a finite part of the macroscopic baths. So by repeatedly obtaining finite-time dynamics in presence of finite-size baths one can reconstruct the full dynamics of the system (we prove this). But, simulating the finite-time dynamics with finite-size baths can still be quite difficult, the difficulty scaling exponentially with the number of degrees of freedom. This exponential growth is essentially due to exponential memory requirement. This is handled by using state-of-the-art tensor network techniques which borrow from the standard idea of data compression, like used daily in computers.
The results with this numerical technique were published in Phys. Rev B, 104, 045417 (2021). They were also presented in several conferences and invited talks across the world (including Republic of Korea, India, UK, Poland, USA).
Subsequently, we realized that the PReB scheme is not just a numerical technique. Instead, a particular driving protocol can be devised with realizes the PReB process experimentally. Intrigued by this, we explored the thermodynamics of such a process. Note that, this is very far from the regime of applicability of standard thermodynamics. So, the notion of thermodynamics had to be extended. We used a quantum information-inspired approach to thermodynamics, that has already been formulated in various previous works by other authors. This led to obtaining 'Periodically refreshed quantum thermal machines', which are quantum thermal machines, based on the PReB scheme. This connects various concepts from quantum information, thermodynamics, condensed matter, statistical physics.
These results are in arxiv:2202.05264 which is accepted for publication in Quantum.
Most state-of-the-art theoretical techniques allow simulations of driven dissipative quantum many-body systems only in cases where one or more of the following conditions hold: (i) either infinite or zero temperature, (ii) either very small or very large non-linearities (interactions), (iii) weak coupling to environment, (iv) either very small or very large voltage bias. Further, most numerical techniques are limited to very small degrees of freedom in the system, and are not scalable to several degrees of freedom in the system. Experimental set-ups, on the other hand, often do not respect any of the above conditions. These conditions are thus quite restrictive and severely limit our understanding of already experimentally realizable situations, and their possible device applications. In this project, we have developed a numerical technique, the PReB scheme, that allows simulations of driven dissipative quantum many-body systems far beyond the above mentioned limitations. In particular this allows simulations with (i) finite temperatures (ii) arbitrary (over a wide range) strengths of non-linearity (iii) arbitrary (over a wide range) strengths of coupling to environment (iv) finite voltage bias. The scheme is also scalable to several degrees of freedom of the system. This thereby gives the formalism to understand various experimental settings which would have been inaccessible to theory before.
One further impact of the project is pushing the boundaries of our understanding of thermodynamics of quantum devices. We know that our standard computing devices like mobiles and laptops gets hot when performing a lot of computation. They therefore need efficient heat management schemes. Similar effects can be expected on quantum devices, like a quantum computer, and hence they also would require efficient heat management schemes. However, standard thermodynamics is for macroscopic, close to equilibrium, systems which are at best very weakly coupled to surrounding environment. The assumptions of standard thermodynamics thus do not hold in quantum devices, which are microscopic, driven out of equilibrium and often strongly coupled to surrounding environments. As a result, the meanings of thermodynamic quantities like 'heat' and 'work' become dubious. Consequently, it has become necessary to extend the notions of standard thermodynamics to driven dissipative quantum many-body systems. We extended the standard notions of thermodynamics to PReB scheme, thereby discovering 'Periodically refreshed quantum thermal machines'. Among various counter-intuitive properties of the 'Periodically refreshed quantum thermal machines' are the facts that they are always far from equilibrium and can utilize the periodic switching of coupling to surrounding environments for useful tasks, like cooling one of the environments. Clearly, this is very far from standard thermodynamic regimes.
These results are imperative to development of quantum technology. Moreover, apart from quantum devices, driven dissipative quantum many-body systems abound across quantum physics, chemistry, biology and engineering, making the results applicable across all these fields.
One further impact of the project is pushing the boundaries of our understanding of thermodynamics of quantum devices. We know that our standard computing devices like mobiles and laptops gets hot when performing a lot of computation. They therefore need efficient heat management schemes. Similar effects can be expected on quantum devices, like a quantum computer, and hence they also would require efficient heat management schemes. However, standard thermodynamics is for macroscopic, close to equilibrium, systems which are at best very weakly coupled to surrounding environment. The assumptions of standard thermodynamics thus do not hold in quantum devices, which are microscopic, driven out of equilibrium and often strongly coupled to surrounding environments. As a result, the meanings of thermodynamic quantities like 'heat' and 'work' become dubious. Consequently, it has become necessary to extend the notions of standard thermodynamics to driven dissipative quantum many-body systems. We extended the standard notions of thermodynamics to PReB scheme, thereby discovering 'Periodically refreshed quantum thermal machines'. Among various counter-intuitive properties of the 'Periodically refreshed quantum thermal machines' are the facts that they are always far from equilibrium and can utilize the periodic switching of coupling to surrounding environments for useful tasks, like cooling one of the environments. Clearly, this is very far from standard thermodynamic regimes.
These results are imperative to development of quantum technology. Moreover, apart from quantum devices, driven dissipative quantum many-body systems abound across quantum physics, chemistry, biology and engineering, making the results applicable across all these fields.