Theses supervised by Prof. Dr. Özgür Esat Müstecaplıoğlu
10 theses · Koç University
Thermal management of atomic and photonic systems
Recent years have seen tremendous progress in developing quantum technologies that rely on the physical systems' quantum features, such as quantum coherence and entanglement. In principle, these quantum systems are not isolated and interact with the environment, which leads to decoherence in which quantum correlations weaken or vanish entirely. The mathematical formulation which describes the system's dynamics in the environment's presence generally requires several approximations. One example is the quantum Markovian master equation based on the perturbative approach in weak system-bath interaction. Typically, a phenomenological approach is adopted in deriving the master equation in which inter-system interactions are ignored, which results in the ``local" dissipation terms in the master equation. We show that such an approach is inconsistent with the laws of thermodynamics in the case of nonlinearly coupled resonators. Instead, the master equation derived from the first principles is consistent, usually termed the ``global" master equation. The heat flow put serious restrictions on the miniaturization of quantum-based technologies. One promising direction can be to power these devices with heat rather than considering the heat flow as a noise source. Accordingly, it is desirable to have efficient models of quantum thermal heat managers which can assist in controlling the heat flow. Following this direction, here, we propose an efficient quantum thermal diode and transistor model that can provide perfect rectification and very large tunable heat amplification, respectively. The dynamics of the system are described by the global master equation, which assists in uncovering the underlying mechanism in these thermal devices. In addition, we show that our model of the quantum thermal transistor, based on two coupled qubits, can also be used as a quantum absorption refrigerator, which is in variance with previous proposals of refrigerators that generally require three-body interaction. It is often required to cool finite quantum systems rather than classical reservoirs. For instance, cooling mechanical resonators to the ground state is a prerequisite for most applications based on mechanical systems in quantum information and quantum communication. However, cooling multiple resonators to the ground state is challenging using typical laser and feedback cooling schemes. To overcome this challenge, we propose a scheme by which simultaneous cooling of multiple resonators is possible. Unlike previous proposals, external control or work input is not required; instead, incoherent thermal drives can cool the resonators. Finally, we investigate the possibility of generating entanglement between uncoupled mechanical resonators, which are only driven by incoherent thermal baths. We show that it is possible to generate significant entanglement between the resonators by judicious choice of thermal baths spectra. The suppression of undesired dissipation and favoring the desired effective two-mode squeezing-like interactions generated by the incoherent interaction with the baths leads to entanglement between the resonators.
Single trapped atom system and its applications in quantum thermal machines
A quantum heat engine is a machine that converts thermal energy to work by following the quantum mechanics laws. In this thesis, I investigate single atom-field interaction and its applications in quantum thermal machines. I show the possibility of exploiting thermodynamic processes for enantiomer detection, which are chiral molecules that exist in right-handed and left-handed conformations. A quantum Otto cycle is employed, in which a chiral molecule described by a three-level system with cyclic optical transitions is considered a working medium. I demonstrate that left and right-handed molecules can be distinguished by evaluating the work distribution in the Otto cycle. Also, I show how quantum signatures can appear in a single-atom heat engine consisting of an atom confined in a tapered trap and subject to hot and cold thermal reservoirs. It is found that lowering the temperature is insufficient to make the single-atom engine of Ref. [Roßnagel et al., 2016] a genuine quantum-enhanced heat engine. I show that it is necessary to make the trap more asymmetric and confined to ensure that quantum correlations cause an enhancement in the power output. A method is presented to generate a dipole trap with a radius of the sub-diffraction limit, which makes the atom more confined. Moreover, I indicate that the single atom-field coupling strength is improved by reducing the trap's radius.
Applications of quantum metrology and thermodynamics in emerging quantum technologies
The emerging field of quantum technologies is poised to revolutionize various aspects of science, engineering, and computing. One of the most promising branches of quantum information sciences is quantum metrology, which plays a pivotal role in modern quantum technologies by enabling ultra-precise measurements that underpin their functionality and performance. At the heart of quantum metrology lies the exploitation of quantum resources such as entanglement which allow for unprecedented levels of sensitivity and resolution. Additionally, optimal design of quantum devices makes it necessary to study the fundamental principles governing energy transfer, work extraction, and entropy production in quantum systems. Hence, quantum thermodynamics offers profound insights into the efficiency limits of energy conversion processes, ultimately shaping the design of quantum technologies. In this thesis, I review my five manuscripts, three of which are on optical quantum metrology and two of which are on thermodynamics of engineered quantum devices, which are presented in chapter 2 to chapter 6. In chapter 2, we calculate the precision bounds of Fock state optical probes for extracting information from an artificial neural network, which mimics the behavior of the retinal network. We shown that Fock state probes yield higher sensitivity than their coherent and thermal counterparts. In chapter 3 we investigate the precision bounds of polarization entangled Bell state for a polarimetric task. Theoretical calculations are accompanied by experimental data. We show that although entanglement provides quantum advantage in terms of precision, environmental noise introduces bias in the estimated values of the parameters which limits the mentioned advantage. In chapter 4 we calculate the precision bounds on estimation of rotation angle due to a birefringent medium in a general polarimetric setup. In our study we take into account several models of depolarization and ordering of polarimetric channels and include the effect of optical losses. Our results show that NOON state probes provide superior metrological performance compared with coherent and anticoherent states as depolarization as diattenuation of the probe is not strong. Even for relatively high depolarization rates, NOON state with small mean photon numbers yield a better precision bound compared with the coherent and anticoherent states. In chapter 5 we investigate the effect of coupling strengths and coherence within a structured environment on the steady-state heat transfer in an engineered biomimetic system, using collision model for simulating the open quantum dynamics. We show that interaction with the environment modulates the energy levels of the system and decreases the transition energy between certain eigenstates, making these transitions more accessible to the hot thermal bath. In chapter 6 we implement counterdiabatic drive to accelerate adiabatic and hot isochoric branches of a quantum Otto engine. Our results for a single cycle show that, taking the control costs into consideration, the heat engine with both adiabatic and isochoric controlled branches reaches a higher power output, albeit with slightly reduced efficiency compared with the engine with counterdiabatic drive only implemented on its adiabatic strokes. However, in limit cycle, it is possible to allocate stroke durations such that the engine with both controlled adiabatic and isochoric branches operates with higher efficiency and power output. Finally, a detailed analysis and discussion of the results for all chapters is given in the conclusions section.
Biyolojik sistemler için kuantum metroloji
This thesis outlines three main projects which link biology, quantum information, and metrology. It culminates with future perspectives on quantum biology and various research related to the brain. The first project begins with an examination of quantum information, moving from theoretical concepts to their practical implementation in biological environments. It tackles the issue of maintaining quantum coherence and entanglement despite the presence of environmental noise in open quantum systems. Geometrical optimization using buffer spins as a protective network of the quantum information in the central spin is introduced. Furthermore, the phenomenon of entanglement in a corresponding biological context is investigated by carrying out preliminary analysis of a more realistic system, the Posner cluster. In the second project, the focus shifts to quantum sensing, with particular attention to the Nitrogen-Vacancy (NV) center, a point defect in diamond. The role of NV centers as sensitive probes is examined in biological contexts, particularly for detecting magnetic fields. The application of spin squeezing to NV centers, when considered as qutrit (three-level) systems, may potentially improve the precision of magnetic field measurements. This precision is quantified using Quantum Fisher Information. Moreover, the integration of a selective bioresponsive material, such as hydrogel, that act as a transducer in the measurement setup could open new avenues to a wider range of biological measurements. The third project explores the use of quantum light to probe biological systems. It examines how quantum mechanics, particularly multipartite photon entanglement, can enhance our understanding of vision. This is achieved through simulations of psychophysical experiments, utilizing entanglement witnesses, a class of observables used to detect entanglement. Starting with bipartite entangled state, and then, generalizing to tripartite case, the probability of seeing of the human eye is determined for a certain range of additive noise levels and visual thresholds. The results shed light on the human eye's capacity to witness entanglement. The three topics covered demonstrate the intertwining relationship between biology and quantum physics. This is further detailed as future perspectives of research by posing some of the most intriguing and fundamental questions of all time in science. A special emphasis of the connection of this relationship to the brain is laid. Eventually, building on such endeavors will become the groundwork of significant potential contributions to future developments in biological and medical sciences.
Advances in quantum computing, quantum error correction, and quantum algorithms
The theoretical framework of quantum computing has promised a considerable advantage in the speed-up of the information processing over the classical computers. It harnesses the theory of quantum mechanics to propose novel frameworks of computing. Several models have been suggested and developed for implementing quantum computers, such as the circuit model of quantum computing, topological quantum computing, and measurement-based quantum computing. We will be concerned with the former model, that is the circuit model of quantum computing. We will first provide a review of the basic axioms of quantum computing that directly rely on those of the theory of quantum mechanics. The circuit model of quantum computation for dealing with computational tasks will be introduced. There are three main problems of concern in this framework including the universality of quantum computing, the advantage of quantum computing over classical computing from the computational complexity point of view, and attempts to counteract the possible effects of noise on a quantum computer, that are studied here. Inspired by some famous quantum algorithms that are proposed in alignment with this model, a recently proposed quantum algorithm for dealing with the problem of testing the linearity of Boolean functions which promises a speed-up over the well-known classical linearity test referred to as the BLR test, will be discussed. We will also discuss the well-known classical algorithm of testing the Boolean functions for being a low-degree polynomial and we may give suggestions on designing quantum algorithms aiming at this algebraic property testing task.
Çoklu foton i̇şlemleri, dolaniklilik ve hibrid sistemlerde kuantum yürüyüşleri:Devre kuantum elekrodinamiği ve nitrojen boşluk merkezleri
In this thesis, we first examine transfer of particle entanglement and spin squeezing between atomic and photonic subsystems in optical cavities coupled by two-photon exchange. Each cavity contains a single atom, interacting with cavity photons with a two-photon cascade transition. Particle entanglement is characterized by evaluating optimal spin squeezing inequalities for the cases of initially separable and entangled two-photon states. It is found that particle entanglement is first generated among the photons in separate cavities and then transferred to the atoms. The underlying mechanism is recognized as an intercavity two-axis twisting spin squeezing interaction, induced by two-photon exchange, and its optimal combination with the intracavity atom-photon coupling. Secondly, we investigate spin squeezing, quantum entanglement, and second-order coherence in two coupled, driven, dissipative, nonlinear cavities. Solving the quantum optical master equation of the system numerically in the steady state, we calculate the zero-time delay second-order correlation function for the coherent, genuine two-mode entanglement parameters, an optimal spin squeezing inequality associated with particle entanglement, concurrence, quantum entropy, and logarithmic negativity. We compare these quantum statistical properties for the cavities coupled with either single- or two-photon exchange. In the final part of the thesis, we propose a quantum-electrodynamics scheme for implementing the discrete-time, coined quantum walk with the walker corresponding to the phase degree of freedom for a quasimagnon field realized in an ensemble of nitrogen-vacancy centers in diamond. The coin is realized as a superconducting flux qubit. Our scheme improves on an existing proposal for implementing quantum walks in cavity quantum electrodynamics by removing the cumbersome requirement of varying drive-pulse durations according to mean quasiparticle number.
Hiperbolik metamalzemelerde kuantum kontrolu
In this thesis, we study atom-photon interactions on quantum level, inside Hyperbolic Metamaterials (HMM). First, the macroscopic Maxwell equations are examined in the light of Green's dyadics. Second, this formalism, combined with Drude-Lorentz model of materials, is used to infer the existence of \textit{Surface Plasmon Polariton} excitations and hyperbolic dispersion in layered HMM by means of \textit{Effective Medium Approximation}. Third, many-body polaritonic Hamiltonian is diagonalized, and, the medium assisted field is found to be dependent on classical Green's tensor, while no reference to microscopic model is needed. Last, as a test case, QED in complex media based on classical Green's tensor formalism is used to calculate single photon excitation probability for an atom embedded in l-HMM system (Ag/Ti$0_{2}$ layers), when it is shed by a time-inverted, conical, single photon pulse. High excitation probabilities are found, yet problem of outcoupling leaves the implementation impractical.
Multi-qubit fuels
In the last decade, there has been a major development to understand the properties of non-thermal baths, which can be used as a fuel for quantum heat engines. The efficiency of such engines can surpass the classical Carnot bound, and these engines can even operate with a single heat bath and an information reservoir. Quantum coherent particle clusters are one of the examples of such non-thermal baths. Decoherence is the major obstacle for utilizing the advantages of quantum coherent fuels. Increasing the number of particles and thus the amount of coherence can overcome this obstacle. However, the analytical studies of such non-thermal reservoirs were investigated only up to three coherent particles, and for the general coherent multi-particle fuels results were obtained numerically. In this thesis, we analytically show how coherences are classified in N-qubit clusters in terms of their interaction with the working fluid. We demonstrate that these coherent N-qubit clusters can thermalize, coherently drive the working mode, or can be used to engineer effective squeezed thermal bath. We show that the steady-state temperature of the working mode can scale linearly or quadratically with the number of the qubits in the cluster. We also construct an Otto engine using our model and show that we can increase efficiency bound. Finally, we propose how we can implement our model in a circuit-QED platform.
Kuantum sistemlerinde karşılıklı olmayan ısı transferi
Abundance of heat makes it a good candidate as an energy resource, but our ability in manipulating heat is so limited. As a new way of heat control, thermal analogs of non-reciprocal electronic devices, such as a diode, transistor, etc., caught attention in many works. Recently, these works started to propose devices in the quantum domain, and the proposed quantum thermal devices, especially diodes as our focus in this thesis, still have optimization problems. In the cases of two interacting qubits diodes, heat rectification is absent for resonant qubits. In this thesis, we consider a quantum thermal diode composed of two interacting qubits, coupled with an optomechanical- like coupling. We derive the global master equation and calculate the heat current for both flat and Ohmic spectral densities to show the diode behavior. Quality of the diode is quantified by a measure, called rectification factor. We numerically calculate the rectification factor for a wide range of system parameters, including weak and strong coupling regimes. We show that the unit rectification factor is obtained for various parameters both in high and low temperature ranges. Most importantly, almost unit rectification is possible even when the qubits have resonant transition frequencies. We explain the physical mechanism leading to all these results, and we show that the mechanism relies on allowed transition and/or bath couplings being asymmetric. We also demonstrate that the asymmetry in transitions is achieved by an asymmetry in free Hamiltonians of subsystems and/or interaction among them. Demonstrations for the sources of asymmetry are demonstrated with two toy models. One of them is a single qubit, which is the smallest possible diode, and the other is a three-level atom. Even though these two systems show diode behaviors, there is very little control of the rectification direction, and two interacting qubits provide versatile control of the diode.
Algoritmik kuantum ısı motorları
In this thesis, we suggest alternative quantum Otto engines, using heat bath algorithmic cooling with partner pairing algorithm instead of isochoric cooling and quantum SWAP operations instead of quantum adiabatic processes. Liquid state nuclear magnetic resonance systems in a single entropy sink are threated as working fluids. The extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke type of alternative quantum Otto engines. The role of the heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two so that a single incoherent energy resource can be harvested and processed using algorithmic quantum heat engine. Our results indicate a path to programmable quantum heat engines as analogues of quantum computers beyond traditional heat engine cycles. We find that for our NMR system example, implementation of quantum algorithmic heat engine stages yields more power due to increased cycle speeds.