Effective two-level reduction of N-level system dissipative quantum dynamics

Paolo Solinas, Mirko Amico, Nino Zanghı̀

Despite the increasing interest, the research field which studies the concepts of work and heat at the quantum level has suffered from two main drawbacks: first, the difficulty to properly define and measure the work, heat, and internal energy variation in a quantum system and, second, the lack of experiments. Here, we report a full characterization of the dissipated heat, work, and internal energy variation in a two-level quantum system interacting with an engineered environment. We use the IBMQ quantum computer to implement the driven system's dynamics in a dissipative environment. The experimental data allow us to construct quasiprobability distribution functions from which we recover the correct averages of work, heat, and internal energy variation in the dissipative processes. Interestingly, by increasing the environment coupling strength, we observe a reduction of the pure quantum features of the energy exchange processes that we interpret as the emergence of the classical limit. This makes the present approach a privileged tool to study, understand, and exploit quantum effects in energy exchanges.

M. Kira, S. W. Koch

Zhongyuan Zhou, Shih‐I Chu, Siyuan Han

Andrei P. Kirilyuk

The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the quantum measurement process. The modified Schroedinger formalism involving multivalued effective dynamical functions reveals the dynamic origin of quantum measurement indeterminacy as the intrinsic instability in the compound system of 'measured object' and (dissipative) 'instrument' with respect to splitting into spatially localised 'realisations'. As a result, the originally wide measured wave catastrophically (and really!) "shrinks" around a random accessible point thus losing all its 'nonlocal properties' with respect to other points/realisations. The dissipativity of one of the interacting objects (serving as 'instrument') is reduced to its (arbitrarily small) openness towards other systems (levels of complexity) and determines the difference between quantum measurement and quantum chaos, the latter corresponding to an effectively isolated system of interacting (micro-) objects. We do not use any assumptions on particular "classical", "macroscopic", "stochastic", etc. nature of the instrument or environment: physical reduction and indeterminacy dynamically appear already in interaction between two microscopic (quantum) deterministic systems, the object and the instrument, possessing just a few degrees of freedom a part of which, belonging to the instrument, should correspond to locally starting, arbitrarily weak excitation. This dynamically indeterminate wave reduction occurs in agreement with the postulates of the conventional quantum mechanics, including the rule of probabilities, which transforms them into consequences of the dynamic uncertainty.

Maria Carolina Nemes, A. F. R. de Toledo Piza

Simon B. Jäger, Ralf Betzholz

Recently, an effective Lindblad master equation for quantum systems whose dynamics are coupled to dissipative bosonic modes was introduced [J\"ager et al., Phys. Rev. Lett. 129, 063601 (2022)]. In this approach, the bosonic modes are adiabatically eliminated, and one can effectively describe the dynamics of the quantum systems. Here, we demonstrate that this effective master equation can also be used to describe cooling in systems with light-matter interactions. We provide two examples: sideband cooling of an optomechanical oscillator in the unresolved as well as resolved sideband regime and cooling of an interacting quantum system, the transverse-field Ising model. We compare our effective description with a full numerical simulation of the composite formed by the quantum system plus bosonic mode and find excellent agreement. In addition, we present how the effective master equation can be extended to the case of nonvanishing mean thermal occupations of the bosonic mode. We use this approach to calculate modifications of the linewidth and frequency for a two-level system coupled to a dissipative thermal bosonic mode. Here, we highlight that our approach allows for a massive reduction of the underlying Liouville-space dimension.