Abstract:
One of the fundamental axioms of quantum mechanics is that observables are self-adjoint or Hermitian operators in a complex Hilbert space. What started as a mathematical curiosity in the late 90s, theoretical investigations into non-Hermitian PT-symmetric Hamiltonians, which emulate open systems with bal- anced gain and loss while producing real eigenspectrums in certain parametric regimes have fledged into an active research field with various experimental real- isations in classical as well as quantum setups. One of the most interesting appli- cations of quantum PT-symmetric two-level systems or qubits is that they show suppressed decoherence when compared to their Hermitian counterparts. This motivates us to study the quantum thermodynamics of PT-symmetric qubits in simple processes to better understand their potential as building blocks for future quantum computers. In this thesis, we primarily study two popular mathematical approaches in literature used to analyze time-dependent PT-symmetric Hamil- tonians, which are called the canonical mapping approach and the non-canonical mapping approach. We then apply them separately to study two thermodynamic problems, namely, the proof of the Jarzynski equality using the non-canonical approach and the efficiency of the quantum Otto engine with a PT-symmetric qubit as the working medium using both approaches. Our findings suggest that it is possible to get higher efficiency and power outputs for these PT-symmetric qubit Otto engines as compared to their Hermitian counterparts.
