Extending bandwidth sensitivity of Rydberg-atom-based microwave electrometry using an auxiliary microwave field

We demonstrate the use of an auxiliary microwave field to extend the bandwidth sensitivity of Rydberg-atom-based microwave electrometry. Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg atom microwave electrometry provide advantageous sensitivity for the resonant detection of microwave (MW) fields because the Stark shift of the target Rydberg state takes the linear form of AT splitting. However, the sensitivity is reduced by several orders of magnitude for detuned MW fields because the Stark shift of the target Rydberg state depends on a weak nonlinear effect. We show that the auxiliary microwave field with appropriate Rabi frequency or detuning could shift the atomic energy levels to bring a particular Rydberg-Rydberg transition of interest for microwave sensing into resonance with the target microwave field. Using the atomic superheterodyne method, we verified the general method that regulates Rydberg energy levels using an auxiliary microwave field. The experimental results of this study confirm that this technique works efficiently for detecting microwave fields detuned by up to 100 MHz from resonance with the field-free Rydberg-Rydberg transition used for sensing. The measurement sensitivity of the detuned target field is increased by a factor of 10 compared with that achieved without the application of the auxiliary dressing field.

Figure 1

Five-level scheme of Rydberg EIT-AT splitting with auxiliary microwave dressed. The detailed energy level diagram in the purple frame is the specific scheme applied to the atomic superheterodyne experiment.

Figure 2

Spectral images of theoretical numerical calculation. (a) When the detuning of the target microwave field is ${\mathrm{\Delta }}_t=2\pi \times 10$ MHz and the detuning of the auxiliary field is ${\mathrm{\Delta }}_a=0$ MHz, spectral regulating effect of different auxiliary microwave electric field Rabi frequency ${\mathrm{\Omega }}_a$. The EIT-AT splitting is symmetric again when ${\mathrm{\Omega }}_a=2\pi \times 21.3$ MHz. (b) EIT-AT splitting spectral images of theoretical numerical calculation before and after auxiliary microwave electric field dressed.

Figure 3

Experimental setup of Rydberg energy level regulation using an auxiliary microwave.

Figure 4

Spectral images of EIT-AT splitting experiment before and after auxiliary microwave electric field dressed. Black solid curve: EIT signal generated by the system when there is no microwave field. Red dotted curve: symmetrical EIT-AT splitting at resonance. Blue dotted curve: asymmetric EIT-AT splitting at detuning ${\mathrm{\Delta }}_{LO}=2\pi \times 14.6$ MHz. Purple dotted curve: the again symmetric EIT-AT splitting after auxiliary field dressed. The EIT-AT splitting is again symmetrical. This indicates that the detuned local microwave field and the target Rydberg-level transition frequency dressed by the auxiliary microwave field is resonated again. Experimental parameters of lock-in amplifier: sensitivity 5 mV, time constant 1 ms.

Figure 5

The best matching curve of the generalized Rabi frequency of the auxiliary microwave field to the local microwave field detuning. Red square dotted line: The demand degree relation of generalized Rabi frequency $\mathrm{\Omega }$ for achieving the best response effect of Rydberg energy level by changing Rabi frequency ${\mathrm{\Omega }}_a$ of auxiliary field. Blue circle dotted line: The demand degree relation of generalized Rabi frequency $\mathrm{\Omega }$ for achieving the best response effect of Rydberg energy level by changing detuning ${\mathrm{\Delta }}_a$ of auxiliary field. Their generally consistent trend degree reflects their equivalence. The demand degree refers to the extent to which we need the ${\mathrm{\Omega }}_a$ or ${\mathrm{\Delta }}_a$ to achieve the best regulation effect.

Figure 6

The influence of auxiliary microwave electric field on beat signal under heterodyne method. The black solid line is the beat signal of the resonance point, the red dotted line is the beat signal of the ${\mathrm{\Delta }}_{\text{LO}}=-2\pi \times 16$ MHz detuning point, and the blue dotted line is the beat signal after the intervention of the best matched auxiliary field of the ${\mathrm{\Delta }}_{\text{LO}}=-2\pi \times 16$ MHz detuning point. The beat amplitude is significantly enhanced after the auxiliary field intervention, and the response of the beat amplitude to the microwave field strength returns to the most sensitive linear effect in resonance. Experimental parameters of lock-in amplifier: sensitivity 2 mV, time constant 100 $\mu \text{s}$.

Figure 7

Response curve of beat frequency signal amplitude before and after auxiliary microwave field intervention under nonresonant heterodyne method within the frequency detuning range from 0 to $-100$ MHz. Black square dotted line: the response relationship between the beat signal amplitude of the ordinary nonresonant heterodyne method and the detuning ${\mathrm{\Delta }}_{\mathrm{LO}}/2\pi$. Red circle dotted line: the response relationship between the amplitude of nonresonant heterodyne beat signal and the detuning ${\mathrm{\Delta }}_{\mathrm{LO}}/2\pi$ under the intervention of auxiliary field. The intervention of auxiliary field provides a wide and high-sensitivity linear response frequency range of 100 MHz. Lower panel: the height of histogram and color bar correspond to optimal matching auxiliary field Rabi frequency and mark the upper limit of our microwave source power with “Power-Max.” Experimental parameters of lock-in amplifier: sensitivity 5 mV, time constant 100 $\mu \text{s}$.

Figure 8

The relationship between the beat signal amplitude and the microwave electric field strength to be measured at the resonance point of ${\mathrm{\Delta }}_{\mathrm{LO}}=0$ MHz and the detuning point of ${\mathrm{\Delta }}_{\mathrm{LO}}=-2\pi \times 22$ MHz by the heterodyne method before and after the auxiliary microwave field intervention. Black square dotted line: at the resonance point, the minimum measurable value is 18 $\mu \mathrm{V}$/cm. Blue triangle dot line: at the detuning point, the minimum measurable value is 180 $\mu \mathrm{V}$/cm. Red circle dotted line: at the detuning point, with the auxiliary microwave field intervention, the minimum measurable value is 18 $\mu \mathrm{V}$/cm. The heterodyne method of auxiliary field intervention can basically reach the measurement limit value at resonance. Panel (b) is a detailed drawing within the scope of panel (a) $E_{\text{SIG}}\le 0.1$ mV/cm. Experimental parameters of lock-in amplifier: sensitivity 2 mV, time constant 100 $\mu \text{s}$.

Figure 9

Comparison diagram of measurement sensitivity with and without auxiliary microwave electric field in the frequency detuning range from 0 to $-100$ MHz. Black square dotted line: the relationship curve between the minimum measurement limit and the detuning ${\mathrm{\Delta }}_{\mathrm{LO}}/2\pi$ without the intervention of auxiliary field. Red circle dot line: the curve of the relationship between the minimum measurement limit and the detuning ${\mathrm{\Delta }}_{\mathrm{LO}}/2\pi$ under the optimal matching auxiliary field intervention. The lower panel: the height of histogram and color bar correspond to optimal matching auxiliary field Rabi frequency, and mark the upper limit of our microwave source power with “Power-Max.” In the experimental detuning interval, the intervention of auxiliary field can basically achieve better measurement sensitivity. Experimental parameters of lock-in amplifier: sensitivity 2 mV, time constant 100 $\mu \text{s}$.