Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipul
ated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly-controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalise the critical spin-field coupling strength, we have observed a four-qubit non-equilibrium quantum phase transition in a dynamical manner, i.e., we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the systems eigenstates. Our observation of the non-equilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition related science, such as scaling behaviours, parity breaking and long-range quantum correlations.
We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the
model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no-degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to unreasonable treatment of the ground state of the model or of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations.
We study the breaking of parity in the spin-boson model and demonstrate unique scaling behavior of the magnetization and entanglement around the critical points for the parity breaking after suppressing the infrared divergence existing inherently in
the spectral functions for Ohmic and sub-Ohmic dissipations. Our treatment is basically analytical and of generality for all types of the bath. We argue that the conventionally employed spectral function is not fully reasonable and the previous justification of quantum phase transition for localization needs to be more seriously reexamined.
We consider a single ion confined in a trap under radiation of two traveling waves of lasers. In the strong-excitation regime and without the restriction of Lamb-Dicke limit, the Hamiltonian of the system is similar to a driving Jaynes-Cummings model
without rotating wave approximation (RWA). The approach we developed enables us to present a complete eigensolutions, which makes it available to compare with the solutions under the RWA. We find that, the ground state in our non-RWA solution is energically lower than the counterpart under the RWA. If we have the ion in the ground state, it is equivalent to a spin dependent force on the trapped ion. Discussion is made for the difference between the solutions with and without the RWA, and for the relevant experimental test, as well as for the possible application in quantum information processing.
