Ground state transition for two-level system coupled with Bose field

Herbert E. Spohn

Biswadeb Dutta, A. M. Jayannavar

Displaced squeezed states are proposed as variational ground states for phonons (Bose fields) coupled to two-level systems (spin systems). We have investigated the zero-temperature phase diagram for the localization-delocalization transition of a tunneling particle interacting with an Ohmic heat bath. Our results are compared with known existing approximate treatments. A modified phase diagram using the displaced squeezed state is presented.

Jay D. Mancini, Vassilios Fessatidis, S.P. Bowen +2 more

Gaoke Hu, Zhiguo Lü, Hai‐Qing Lin +1 more

The unitary transformation method is used to study the properties of the polaritonic states and Bose-Einstein condensation in the Rabi lattice model, where the on-site two-level systems (TLSs) are coupled with the intersite hopping photons. It is shown that the counter-rotating coupling (CRC) between TLS and photon, which breaks down the conservation of the excitation numbers, may induce a long-range Ising-like interaction among intersite TLSs. We have shown that the coupled TLSs and photons are hybridized to form the polaritonic states, and the corresponding ground state and polaritonic excitation spectra are calculated by diagonalizing our transformed Hamiltonian. When the photon hopping $J$ is weak, the excitation spectrum is gapped. But the gap decreases with increasing $J$, and at critical value $J={J}_{c}$ the gap becomes zero at the $\mathrm{\ensuremath{\Gamma}}$ point and the ground state becomes instable. Thus, ${J}_{c}$ is the phase transition point where the polaritons are condensed at the $\mathrm{\ensuremath{\Gamma}}$ point to form the delocalized superradiant phase. The results show that the larger detuning between TLS and photon favors the disorder insulator phase, which requires the stronger ${J}_{c}$ to get the long-range order phase. The phase diagram of the delocalized superradiant phase transition has been obtained where there are no Mott lobes since the CRC breaks down the number conservation. The ground state and the excitation spectra of the delocalized superradiant phase are also calculated. It is shown that in the delocalized superradiant state the order parameter is the nonzero ground-state average of the photon annihilation operator. The polaritonic excitation has a finite excitation gap because the CRC breaks down the number conservation but leaves only a discrete symmetry, the parity conservation.

L. Reatto

V. M. Kovalev, Wang-Kong Tse

We develop a microscopic theory for the relaxation dynamics of an optically pumped two-level system (TLS) coupled to a bath of weakly interacting Bose gas. Using Keldysh formalism and diagrammatic perturbation theory, expressions for the relaxation times of the TLS Rabi oscillations are derived when the boson bath is in the normal state and the Bose-Einstein condensate (BEC) state. We apply our general theory to consider an irradiated quantum dot coupled with a boson bath consisting of a two-dimensional dipolar exciton gas. When the bath is in the BEC regime, relaxation of the Rabi oscillations is due to both condensate and non-condensate fractions of the bath bosons for weak TLS-light coupling and pre dominantly due to the non-condensate fraction for strong TLS-light coupling. Our theory also shows that a phase transition of the bath from the normal to the BEC state strongly influences the relaxation rate of the TLS Rabi oscillations. The TLS relaxation rate is approximately independent of the pump field frequency and monotonically dependent on the field strength when the bath is in the low-temperature regime of the normal phase. Phase transition of the dipolar exciton gas leads to a non-monotonic dependence of the TLS relaxation rate on both the pump field frequency and field strength, providing a characteristic signature for the detection of BEC phase transition of the coupled dipolar exciton gas.