Non-Linearities In Atomic Quantum Receivers: Harmonic And Intermodulation Distortion

The gist: This work reports on measurements and characterization of non-linear behavior and spurious response in Rydberg atomic RF receivers, revealing that under suitable operating conditions, these receivers can exhibit a suppression of harmonic and inter-modulation distortion relative to classical receiver mixer amplifiers.

Introduction to the Problem

Rydberg atom-based radio-frequency (RF) sensors are a rapidly advancing quantum technology offering transformative capabilities in RF applications. A critical aspect remains unexplored is the non-linear behavior of Rydberg atom receivers and their harmonic and intermodulation distortion performance in RF signal reception. This study addresses this gap by reporting on measurements and characterizations of non-linear behavior and spurious response in Rydberg atomic RF receivers. The authors translate traditional concepts from RF engineering to quantum Rydberg atomic sensors and develop analogous testing procedures suitable for atomic receivers.

Atomic Receiver Testing Setup

The test setup for single-tone and two-tone testing of a Rydberg atomic RF heterodyne receiver is illustrated in Figure 1. Two signal tones at frequencies F1 and F2 are generated and combined with the atomic receiver reference local oscillator (LO) at frequency FLO used in phase-sensitive atomic RF heterodyne reception. The three frequencies are generated by three different signal generators synchronized to a rubidium clock, allowing independent frequency and power control of each signal tone and the LO. The atomic vapor is a cesium gas held at room temperature in a glass cell. Multi-photon Rydberg spectroscopy and electromagnetically-induced transparency (EIT) are used to access RF-field sensitive Rydberg states of the cesium gas with two counter-propagating laser beams at 852 nm (probe beam) and 510 nm (coupler beam). The atomic heterodyne receiver response to the applied tones is measured on the SA at intermediate frequencies f1 = FLO − F1 and f2 = FLO − F2, as well as at overtones and mixing products of f1 and f2.

Single-Tone Testing: Selectivity and Roll-off

A single-tone measurement characterizes the atomic receiver selectivity, IF bandwidth, and filter roll-off for an SHF-band signal tone. The response of the atomic receiver to a tone at frequency F and field amplitude EF = 0.017 V/m(−35.4 dBV/m) is measured as a function of its frequency detuning in the IF f = F − FLO relative to the receiver LO frequency FLO = 9.9376 GHz. The measured IF bandwidths are given in Table I. In Figure 2c, the atomic receiver filter roll-off plot of the signal rejection ratio in dBc versus f shows linear fits yielding 10 dB/decade for f 1.1 MHz. Second and third harmonics emerge at frequencies (and signal levels) f2 = 200 kHz (29.5 dB) and f3 = 300 kHz (12.8 dB), respectively, as a result of harmonic mixing of the tone and local oscillator fields by the non-linear atomic medium. The second order intercept (IP2) and third order intercept (IP3) of the harmonic distortion products are also obtained, and nearly coincide at the F1 field strength of E1=12.5 dBV/m.

Two-Tone Testing: Intermodulation Distortion

Intermodulation distortion is investigated by simultaneously applying F1 and a second tone, F2. In condition (1) with ∆F/F = 10−6, IMD peaks up to the 8th order are clearly identified. In condition (2) with ∆F/F = 10−4, fewer IMD peaks are observed because the large ∆F allows only a few IMD frequencies within the atomic IF response bandwidth. The IP3 points for the ∆F/F = 10−4 measurements are determined to be 19.3 dBV/m and 11.9 dBV/m for f1 and f2, respectively <ref:2412.

1. Non-linear response modeling for atomic receivers allows AI systems to predict specific distortion products, such as harmonic generation and intermodulation distortion, based on incident RF power levels and frequency offsets in the atomic medium. This capability enables AI to design receiver front-ends that are inherently more robust against unwanted interfering signals by anticipating where non-linear effects will manifest.

2. Development of a figure of merit for intermodulation distortion (FoM=IP3-P1dB) allows AI systems to benchmark the performance of both quantum and classical receivers, identifying specific operational regimes where atomic receivers offer superior tolerance to interference, such as the observed 10 dB advantage compared to classical low-noise amplifiers.

3. The characterization of intermediate frequency (IF) bandwidths and filter roll-off provides AI with a detailed map of the receiver's selectivity across different operating conditions, allowing for the design of adaptive filtering algorithms that optimally reject specific interference frequencies based on the measured spectral shape.

4. Modeling the time-dependent solution using Lindblad master equation allows AI to simulate complex quantum dynamics, enabling its use in designing secure communication modalities where non-linear responses can be switched between discrete spectra for coding or physical frequency hopping.

5. The observation that the slopes of the second and third harmonics are close to 2 and 3, the values expected for semiconductor-based systems suggests that AI can be trained on these scaling laws to generalize performance predictions across different atomic receiver configurations, even when quantitative parameters like IP3 vary with experimental setup.

Rydberg sensors offer a unique approach to radio frequency (RF) detection, leveraging the high sensitivity and quantum properties of highly-excited atomic states to achieve performance levels beyond classical technologies. Non-linear responses and distortion behavior in Rydberg atom receivers are critical to evaluating and establishing performance metrics and capabilities such as spur-free dynamic range and tolerance to unwanted interfering signals. We report here on the measurement and characterization of non-linear behavior and spurious response of a Rydberg atomic heterodyne receiver. Single-tone and two-tone testing procedures are developed and implemented for measurement of harmonic and inter-modulation distortion in Rydberg atomic receivers based on multi-photon Rydberg spectroscopy and radio-frequency heterodyne signal detection and demodulation in an atomic vapor. For a predetermined set of atomic receiver parameters and RF carrier wave in the SHF band near-resonant to a cesium Rydberg transition, we measure and characterize atomic receiver selectivity, bandwidth, roll-off, compression point (P1dB), second-order (IP2) and third-order (IP3) intercepts, and spur-free dynamic range. Receiver intermodulation distortion is characterized for the case of an interfering signal wave applied at two frequency offsets relative to the near-resonant reference local oscillator, ΔF/F= 10-4 at 6dB and 10-6 at 22dB single-tone bandwidths, respectively. We observe that under suitable operating conditions the atomic receiver can exhibit a suppression of harmonic and inter-modulation distortion relative to that of classical receiver mixer amplifiers. Finally, we describe how the non-linear behaviors of atomic receivers can provide unique, controllable RF signatures inaccessible by classical counterparts and propose their use to realize secure communication modalities and applications.