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We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. This will provide the basis for the experimental study of the process of decoherence in a quantum system. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer the coupling and select the master equation describing the motion of the ion.
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We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify itss accuracy.
Recent advances illustrate the power of reservoir engineering in applications to many-body systems, such as quantum simulators based on superconducting circuits. We present a framework based on kinetic equations and noise spectra that can be used to understand both the transient and long-time behavior of many particles coupled to an engineered reservoir in a number-conserving way. For the example of a bosonic array, we show that the non-equilibrium steady state can be expressed, in a wide parameter regime, in terms of a modified Bose-Einstein distribution with an energy-dependent temperature.
Light-matter coupling involving classical and quantum light offers a wide range of possibilities to tune the electronic properties of correlated quantum materials. Two paradigmatic results are the dynamical localization of electrons and the ultrafast control of spin dynamics, which have been discussed within classical Floquet engineering and in the deep quantum regime where vacuum fluctuations modify the properties of materials. Here we discuss how these two extreme limits are interpolated by a cavity which is driven to the excited states. In particular, this is achieved by formulating a Schrieffer-Wolff transformation for the cavity-coupled system, which is mathematically analogous to its Floquet counterpart. Some of the extraordinary results of Floquet-engineering, such as the sign reversal of the exchange interaction or electronic tunneling, which are not obtained by coupling to a dark cavity, can already be realized with a single-photon state (no coherent states are needed). The analytic results are verified and extended with numerical simulations on a two-site Hubbard model coupled to a driven cavity mode. Our results generalize the well-established Floquet-engineering of correlated electrons to the regime of quantum light. It opens up a new pathway of controlling properties of quantum materials with high tunability and low energy dissipation.
An experimental demonstration of a non-classical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary oscillator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5 - 0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$ and for support temperatures of T $approx$ 25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed state via measurements of the excited state population. Furthermore, by extending this measurement procedure a complete quantum state tomography of the resonator state can be performed. This provides a universal tool to detect a large variety of different states and to prove the quantum nature of a nanomechanical oscillator.
Reservoir engineering is the term used in quantum control and information technologies to describe manipulating the environment within which an open quantum system operates. Reservoir engineering is essential in applications where storing quantum information is required. From the control theory perspective, a quantum system is capable of storing quantum information if it possesses a so-called decoherence free subsystem (DFS). This paper explores pole placement techniques to facilitate synthesis of decoherence free subsystems via coherent quantum feedback control. We discuss limitations of the conventional `open loop approach and propose a constructive feedback design methodology for decoherence free subsystem engineering. It captures a quite general dynamic coherent feedback structure which allows systems with decoherence free modes to be synthesized from components which do not have such modes.
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