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Quantum technological applications using dissipative many-body dynamics

Meghana Raghunandan

Published Jan 1, 2020• 1 citation
Publisher

Abstract

Quantum systems cannot always be treated as isolated from their surroundings since this is an idealization which is not always true. Though theoretical analysis of open quantum systems poses great challenges as one needs to treat many-particle quantum systems as a whole, the system-environment interactions often lead to many interesting effects that are not observed in closed systems. The dissipation of a quantum system is not always a disadvantage and, in fact, if exploited properly in combination of coherent driving, one can steer the system into a desired state. This dissipation driven quantum state engineering technique finds its applications in novel technologies such as quantum computing, quantum simulation, and quantum metrology. In this thesis, we focus on the latter two, and show that using dissipative channels allows us to build quantum devices that have considerable advantages over their entirely coherent analogues. Simulation of many-body problems on a quantum simulator will unlock the potential to provide great insights into a large number of systems especially those that are computationally intractable or experimentally challenging. The two crucial steps towards the successful functioning of quantum simulation are the initialization of the quantum simulators i.e, preparing the system in a known initial state, and the Hamiltonian engineering. While there have been many experiments demonstrating the implementation of the Hamiltonian dynamics on the quantum simulator, work still needs to be done on the problem of preparing the simulator in a suitable quantum state. This is exactly our aim here and we propose a protocol to cool a given system into the ground state of a black-box spin Hamiltonian. The central idea is to use a dissipatively driven auxiliary spin to pull out the excitations in the system, eventually cooling it to its ground state. We show that already a single auxiliary spin is efficient in cooling the quantum simulator to a low-energy state of largely arbitrary Hamiltonians as the resources scale only polynomially with the system size. We also show that our scheme of sympathetic cooling is robust against additional sources of decoherence. The second part of the thesis deals with nanoscale quantum sensing using dissipative first order transition in the magnetization of a system of nitrogen-vacancy point defect centers in diamond. The sensitivity of a generic quantum sensor with non-interacting particles scales as the square root of the number of particles. Therefore, a sensor with large number of particles displays a better sensitivity. However, in the interest of nanoscale sensing, having a large number of particles implies that they are closely packed next to each other. At such high densities, the particles interact strongly with each other posing great challenges to the sensing process. Here, we show that these interactions can in fact be used to trigger a first order phase transition when coupled with controlled dissipation in the system. We study the properties of the phase transition using two- and three-dimensional setups to build a nanoscale quantum sensor that is especially robust against typical disorder imperfections or additional decoherence processes, with the sensitivity not being severely limited by the T2 decoherence time. Since our sensing protocol does not assume too many microscopic details of the process, one can easily apply this to other areas of quantum sensing and metrology. These results especially highlight the fact that dissipation in quantum systems, that is normally considered unwanted, can in fact be a powerful tool that allows us to enable a large list of quantum technologies in the future.

DOI
10.15488/9859

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Quantum systems cannot always be treated as isolated from their surroundings since this is an idealization which is not always true. Though theoretical analysis of open quantum systems poses great challenges as one needs to treat many-particle quantum systems as a whole, the system-environment interactions often lead to many interesting effects that are not observed in closed systems. The dissipation of a quantum system is not always a disadvantage and, in fact, if exploited properly in combination of coherent driving, one can steer the system into a desired state. This dissipation driven quantum state engineering technique finds its applications in novel technologies such as quantum computing, quantum simulation, and quantum metrology. In this thesis, we focus on the latter two, and show that using dissipative channels allows us to build quantum devices that have considerable advantages over their entirely coherent analogues. Simulation of many-body problems on a quantum simulator will unlock the potential to provide great insights into a large number of systems especially those that are computationally intractable or experimentally challenging. The two crucial steps towards the successful functioning of quantum simulation are the initialization of the quantum simulators i.e, preparing the system in a known initial state, and the Hamiltonian engineering. While there have been many experiments demonstrating the implementation of the Hamiltonian dynamics on the quantum simulator, work still needs to be done on the problem of preparing the simulator in a suitable quantum state. This is exactly our aim here and we propose a protocol to cool a given system into the ground state of a black-box spin Hamiltonian. The central idea is to use a dissipatively driven auxiliary spin to pull out the excitations in the system, eventually cooling it to its ground state. We show that already a single auxiliary spin is efficient in cooling the quantum simulator to a low-energy state of largely arbitrary Hamiltonians as the resources scale only polynomially with the system size. We also show that our scheme of sympathetic cooling is robust against additional sources of decoherence. The second part of the thesis deals with nanoscale quantum sensing using dissipative first order transition in the magnetization of a system of nitrogen-vacancy point defect centers in diamond. The sensitivity of a generic quantum sensor with non-interacting particles scales as the square root of the number of particles. Therefore, a sensor with large number of particles displays a better sensitivity. However, in the interest of nanoscale sensing, having a large number of particles implies that they are closely packed next to each other. At such high densities, the particles interact strongly with each other posing great challenges to the sensing process. Here, we show that these interactions can in fact be used to trigger a first order phase transition when coupled with controlled dissipation in the system. We study the properties of the phase transition using two- and three-dimensional setups to build a nanoscale quantum sensor that is especially robust against typical disorder imperfections or additional decoherence processes, with the sensitivity not being severely limited by the T2 decoherence time. Since our sensing protocol does not assume too many microscopic details of the process, one can easily apply this to other areas of quantum sensing and metrology. These results especially highlight the fact that dissipation in quantum systems, that is normally considered unwanted, can in fact be a powerful tool that allows us to enable a large list of quantum technologies in the future.
Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.
Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.
The sensing of external fields using quantum systems is a prime example of an emergent quantum technology. Generically, the sensitivity of a quantum sensor consisting of N independent particles is proportional to sqrt[N]. However, interactions invariably occurring at high densities lead to a breakdown of the assumption of independence between the particles, posing a severe challenge for quantum sensors operating at the nanoscale. Here, we show that interactions in quantum sensors can be transformed from a nuisance into an advantage when strong interactions trigger a dissipative phase transition in an open quantum system. We demonstrate this behavior by analyzing dissipative quantum sensors based upon nitrogen-vacancy defect centers in diamond. Using both a variational method and a numerical simulation of the master equation describing the open quantum many-body system, we establish the existence of a dissipative first order transition that can be used for quantum sensing. We investigate the properties of this phase transition for two- and three-dimensional setups, demonstrating that the transition can be observed using current experimental technology. Finally, we show that quantum sensors based on dissipative phase transitions are particularly robust against imperfections such as disorder or decoherence, with the sensitivity of the sensor not being limited by the T_{2} coherence time of the device. Our results can readily be applied to other applications in quantum sensing and quantum metrology where interactions are currently a limiting factor.
Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.
The controlled preparation of quantum many-body states is a central challenge for quantum technologies. While preparing target states coherently is possible in principle, it is often fragile and experimentally demanding. Dissipative state preparation, where engineered environments drive the system toward desired steady states, provides a complementary and powerful paradigm. This thesis explores dissipative methods for preparing complex many-body states along three distinct directions. First, we investigate the dissipative stabilization of injective matrix product states (MPS). Injective MPS are particularly well suited for dissipative preparation because they arise as ground states of frustration-free parent Hamiltonians, allowing for tailored jump operators to steer the system directly into the target state. We showcase the surprising result that such state preparation works even in the dilute limit where steering only acts on a single link. Moreover, we introduce a formalism for engineering additional coherent interactions, extending the set of accessible states. Second, and complementary to steering, we develop and analyze a universal cooling scheme capable of preparing ground states even in frustrated quantum systems. In contrast to steering methods, universal cooling can overcome the glass floor that forbids steering methods to prepare such frustrated ground states. A key insight here is that the presented cooling scheme is completely system-agnostic making it extremely robust. Finally, we pursue dressing of the system eigenstates by means of either classical drives or coherent interactions as a means to influence the action of dissipation on the system. Focusing first on time-dependent systems, we propose a generalized numerical implementation of non-adiabatic master equations suitable for the use of optimal control tools. Additionally, we investigate how the collective coupling between a spin ensemble and a cavity can steer the system into a spin-squeezed steady state. Together, these three avenues illustrate how tailored dissipative dynamics can extend the frontier of many-body state preparation, from stabilizing injective MPS to cooling complex frustrated systems and generating non-classical steady states in the dressed framework.
Decoherence and errors appear among the main challenges to implement successful quantum technologies. In this thesis I discuss the application of some general tools and principles that may be valuable resources to develop robust technologies, with applications in quantum sensing and quantum simulation. Firstly, we employ suitable periodically driving fields acting on the Ising model in order to tailor spin-spin interactions depending on the spatial direction of the bonds. In this way, we are able to simulate the quantum compass model on a square lattice. This system exhibits topological order and a doubly degenerate ground state protected against local noise. A possible implementation of this proposal is outlined for atomic quantum simulators. Secondly, we exploit two general working principles based on spontaneous symmetry breaking and criticality that may be beneficial to achieve robust quantum sensors, particularly appropriate for quantum optical dissipative systems. A concrete application is given for a minimal model: a single qubit laser. It is shown how the precision in parameter estimation is enhanced as the incoherent pumping acting on the qubit increases, and also when the system is close to the lasing critical point. Finally, classical long-range correlations in lattice systems are shown to provide us with an additional resource to be used in robust sensing schemes. The previous setup is extended to a lattice of single qubit lasers where interactions are incoherent. Under the right conditions, we show that a Heisenberg scaling with the number of probes can be accomplished.