Two-level systems (TLS) in amorphous materials limit coherence times of a number of solid-state quantum devices. Interactions between TLS become prominent below 100 mK, but the coupling mechanism and statistical properties are still unclear. Here we determine the homogeneous linewidth of ytterbium ions $({\mathrm{Yb}}^{3+})$ in silica glass at 10--80 mK by using photon echo techniques as a probe of TLS. First, the homogeneous linewidth can be reduced by applying a magnetic field of 0.3 T. This effect is due to reduced magnetic interactions between adjacent ${\mathrm{Yb}}^{3+}$ . Secondly, we observe saturation of the linewidth below 50 mK to a level of approximately 30 kHz, which is much larger than the lifetime-limited value of 0.2 kHz. This saturation behavior is in conflict with the coupling to independent TLS. We show that this effect can be explained by coherently coupled TLS.Two-level systems (TLS) in amorphous materials limit coherence times of a number of solid-state quantum devices. Interactions between TLS become prominent below 100 mK, but the coupling mechanism and statistical properties are still unclear. Here we determine the homogeneous linewidth of ytterbium ions $({\mathrm{Yb}}^{3+})$ in silica glass at 10--80 mK by using photon echo techniques as a probe of TLS. First, the homogeneous linewidth can be reduced by applying a magnetic field of 0.3 T. This effect is due to reduced magnetic interactions between adjacent ${\mathrm{Yb}}^{3+}$. Secondly, we observe saturation of the linewidth below 50 mK to a level of approximately 30 kHz, which is much larger than the lifetime-limited value of 0.2 kHz. This saturation behavior is in conflict with the coupling to independent TLS. We show that this effect can be explained by coherently coupled TLS.

arXiv:1811.05248Physical review. B./Physical review. BJan 29, 20208 citations

TWO-LEVEL SYSTEM IN A TIME-DEPENDENT FIELD

WORLD SCIENTIFIC eBooksFeb 1, 20240 citations

Exactly solvable time-dependent models of two interacting two-level systems

Roberto Grimaudo, ANTONINO MESSINA, Hiromichi Nakazato

Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional subdynamics. Each of the subdynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional subdynamics. Each of the subdynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.

arXiv:1604.04519Physical Review AAug 9, 201640 citations

Time-dependent N-Level Systems

J. Aliaga, J. L. Gruver, Araceli N. Proto

Springer eBooksJan 1, 19930 citations

Piecewise time-independent procedure to control two-level systems

J. Kuhn, M. G. E. da Luz

We present a general and mathematically simple method to control two-level systems. It is based on a piecewise time-independent procedure. We assume that some parameters of an external interaction potential can be rapidly switched at specified time instants, and then kept constant during small time intervals $\mathrm{\ensuremath{\Delta}}t$. By properly setting the parameter values, obtained from algebraic, instead of differential or integral, equations, we can drive the time evolution of arbitrary observables. We illustrate the approach with some examples and discuss important technical aspects, relevant in real concrete situations, such as the robustness of the method to errors in the control parameter values, the influence of the switching mechanism transient times, the appropriate choice for the $\mathrm{\ensuremath{\Delta}}t$'s, and so on.We present a general and mathematically simple method to control two-level systems. It is based on a piecewise time-independent procedure. We assume that some parameters of an external interaction potential can be rapidly switched at specified time instants, and then kept constant during small time intervals $\mathrm{\ensuremath{\Delta}}t$. By properly setting the parameter values, obtained from algebraic, instead of differential or integral, equations, we can drive the time evolution of arbitrary observables. We illustrate the approach with some examples and discuss important technical aspects, relevant in real concrete situations, such as the robustness of the method to errors in the control parameter values, the influence of the switching mechanism transient times, the appropriate choice for the $\mathrm{\ensuremath{\Delta}}t$'s, and so on.

Physical Review AMay 17, 200711 citations

({\mathrm{Yb}}^{3+})

in silica glass at 10--80 mK by using photon echo techniques as a probe of TLS. First, the homogeneous linewidth can be reduced by applying a magnetic field of 0.3 T. This effect is due to reduced magnetic interactions between adjacent

{\mathrm{Yb}}^{3+}

. Secondly, we observe saturation of the linewidth below 50 mK to a level of approximately 30 kHz, which is much larger than the lifetime-limited value of 0.2 kHz. This saturation behavior is in conflict with the coupling to independent TLS. We show that this effect can be explained by coherently coupled TLS.