Multiresonator quantum memory

In this paper we present universal broadband multiresonator quantum memory based on the spatial-frequency combs of the microresonators coupled with a common waveguide. We find a Bragg-type impedance matching condition for the coupling of the microresonators with a waveguide field that provides an efficient broadband quantum storage. The analytical solution obtained for the microresonator fields enables sustainable parametric control of all the memory characteristics. We also construct an experimental prototype of the studied quantum memory in the microwave spectral range that demonstrates basic properties of the microwave microresonators, their coupling with a common waveguide, and independent control of the microresonator frequencies. Experimentally observed narrow lines of the microresonators confirm the possibility of multiresonator quantum memory implementation.

Figure 1

Spatial scheme of the MR QM: 1–6 are single-mode microwave microresonators with distance $\lambda /2$ between the nearest ones; the microresonators contain dielectric insertions, which ensure the smallness of their spatial sizes in comparison with $\lambda$; and wavy lines represent the propagating electromagnetic fields interacting with the microresonators.

Figure 2

Quantum efficiency ${\eta }_0=4{\tilde{g}}^2/{(1+{\tilde{g}}^2)}^2$ vs the dimensionless coupling constant $\tilde{g}={(\pi \mathrm{\Gamma }/2\mathrm{\Delta })}^{1/2}$; the maximum efficiency $\tilde{g}=1$ corresponds to the Bragg-impedance matching condition.

Figure 3

Current efficiency ${\eta }_1\left(t\right)$ over time $t$ in units of $2\pi /\mathrm{\Delta }$ for $N=6$. The time interval $t\in [0,\pi /\mathrm{\Delta }]$ corresponds to half the storage phase.

Figure 4

Normalized intensity of echo pulse emission $I_1\left(t\right)={\partial }_t{\eta }_1\left(t\right)$ as a function of time $t$ in units of $2\pi /\mathrm{\Delta }$ for $N=6$; the pulse duration is about $\delta t_s\sim 2\pi /N\mathrm{\Delta }$, which allows the use of short pulses.

Figure 5

Current efficiencies of the echo emission ${\eta }_1\left(t\right)$ over time $t$ in units of $2\pi /\mathrm{\Delta }$ for $N=6$ at the matching condition (7). The blue dotted line shows the free evolution and the red solid line the evolution with increased lifetime of the stored pulse due to the alignment of the microresonator frequencies ($\mathrm{\Delta }=0$) during the time interval $T=2\pi /\mathrm{\Delta }$.

Figure 6

Experimental prototype of the MR scheme: The waveguide is connected with six cylindric metallic resonators, the frequencies of which can be tuned using the handles fixing the lengths of the cylinders.

Figure 7

Controllable frequency spectrum of resonator lines in logarithmic scale: The distance $\mathrm{\Delta }$ between the closest frequencies is (a) 5 MHz, (b) 10 MHz, and (c) 15 MHz.