Strong-coupling cavity QED using rare-earth-metal-ion dopants in monolithic resonators: What you can do with a weak oscillator

Abstract

We investigate the possibility of achieving the strong coupling regime of cavity quantum electrodynamics using rare earth ions as impurities in monolithic optical resonators. We conclude that due to the weak oscillator strengths of the rare earths, it may be possible but difficult, to reach the regime where the single photon Rabi frequency is large compared to both the cavity and atom decay rates. However reaching the regime where the saturation photon and atom numbers are less than one should be much more achievable. We show that in this 'bad cavity' regime, transfer of quantum states and an optical phase shift conditional on the state of the atom is still possible, and suggest a method for coherent detection of single dopants.

Coupling of erbium dopants to yttrium orthosilicate photonic crystal cavities for on-chip optical quantum memories

“…This is half the size of the value in McAuslan et al 16 for D 2 polarization due to the factor of two difference between absorption coefficient for light polarized along the D 1 and D 2 directions. Following the results from McAuslan et al, 16 we find the spontaneous emission rate that we would expect from only this decay path to be 10.03 Hz. Comparing this value to the measured excited state decay rate of 87.7 Hz (11.4 ms lifetime), we determine that the branching ratio for Er:YSO in our cavity is $0.11.…”

“…We estimate the branching ratio by comparing the expected emission rate, computed from the 1536 nm transition dipole moment, and the measurable 1/11.4 ms spontaneous decay rate. 16 For this calculation, we use the maximum absorption coefficient 24.5 cm À1 with FWHM of 510 MHz for a 0.02% erbium ion dopant density given an electric field polarized along the D 1 direction from B€ ottger et al 15 to compute an oscillator strength f 12 ¼ 1.095 Â 10 À7 . This is half the size of the value in McAuslan et al 16 for D 2 polarization due to the factor of two difference between absorption coefficient for light polarized along the D 1 and D 2 directions.…”

“…16 For this calculation, we use the maximum absorption coefficient 24.5 cm À1 with FWHM of 510 MHz for a 0.02% erbium ion dopant density given an electric field polarized along the D 1 direction from B€ ottger et al 15 to compute an oscillator strength f 12 ¼ 1.095 Â 10 À7 . This is half the size of the value in McAuslan et al 16 for D 2 polarization due to the factor of two difference between absorption coefficient for light polarized along the D 1 and D 2 directions. Following the results from McAuslan et al, 16 we find the spontaneous emission rate that we would expect from only this decay path to be 10.03 Hz.…”

“…16 This was compared to the decay rate for ions in the cavity when the cavity is resonant with the ions. In this case, two exponential decays were fit, analogous to the fitting procedure by Gong et al, 17 and one of the decay curves had a time constant fixed at the bulk lifetime.…”

Coupling erbium dopants in yttrium orthosilicate to silicon photonic resonators and waveguides

“…However, these long optical coherence times arise from a low oscillator strength, which results in weak interaction with control fields and photonic qubits. It has been shown in theory and experiment that optical resonators can increase the coupling strength between the optical field and the ions [12,13]. Using small cavities [14] and large ensembles, the strong coupling regime can be reached [15].…”