Stimulated Emission of Signal Photons from Dark Matter Waves

Open Access

Stimulated Emission of Signal Photons from Dark Matter Waves

Ankur Agrawal, Akash V. Dixit, Tanay Roy, Srivatsan Chakram, Kevin He, Ravi K. Naik, David I. Schuster, and Aaron Chou

Phys. Rev. Lett. 132, 140801 – Published 3 April 2024

Abstract

The manipulation of quantum states of light has resulted in significant advancements in both dark matter searches and gravitational wave detectors. Current dark matter searches operating in the microwave frequency range use nearly quantum-limited amplifiers. Future high frequency searches will use photon counting techniques to evade the standard quantum limit. We present a signal enhancement technique that utilizes a superconducting qubit to prepare a superconducting microwave cavity in a nonclassical Fock state and stimulate the emission of a photon from a dark matter wave. By initializing the cavity in an $| n = 4 ⟩$ Fock state, we demonstrate a quantum enhancement technique that increases the signal photon rate and hence also the dark matter scan rate each by a factor of 2.78. Using this technique, we conduct a dark photon search in a band around 5.965 GHz ( $24.67 μ eV$ ), where the kinetic mixing angle $ε \geq 4.35 \times 10^{- 13}$ is excluded at the 90% confidence level.

Received 17 July 2023
Accepted 26 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.140801

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Dark matter Machine learning Particle dark matter Quantum circuits Quantum coherence & coherence measures Quantum control Quantum feedback Quantum measurements Quantum metrology Quantum protocols Quantum state transfer Weak values & weak measurements

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyGravitation, Cosmology & Astrophysics

Authors & Affiliations

Ankur Agrawal ^1,2,3,*, Akash V. Dixit ^1,2,3,†, Tanay Roy ^1,2,‡, Srivatsan Chakram^1,2,4,§, Kevin He ^1,2, Ravi K. Naik⁵, David I. Schuster^1,2,6,7, and Aaron Chou⁸

¹James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
²Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
³Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA
⁴Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
⁵Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁶Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
⁷Department of Applied Physics, Stanford University, Stanford, California 94305, USA
⁸Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

^*ankur.agrawal92@gmail.com Present address: AWS Center for Quantum Networking, Boston, Massachusetts 02145, USA.
^†Present address: National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
^‡Present address: Superconducting Quantum Materials and Systems Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA.
^§Present address: Department of Physics and Astronomy, Rutgers, the State University of New Jersey, Piscataway, New Jersey 08854, USA.

Article Text

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Supplemental Material

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References

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Issue

Vol. 132, Iss. 14 — 5 April 2024

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Images

Figure 1
Fock state preparation in a cavity dispersively coupled to a transmon qubit. (a) A schematic of the multimode flute cavity showing the location of the storage cavity (red), readout cavity (green), and transmon chip (blue) with an SEM image of the Josephson junction (see cavity fabrication and surface preparation in [33]). (b) Fock states with up to $n = 4$ are created using GRAPE method and characterized by measuring qubit spectroscopy (top) and Wigner tomography (bottom) [34]. Successful Fock state generation is evident from single peaks in spectroscopy and alternating negative and positive rings in the tomography (see Supplemental Material [30] Sec. D for details).
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Figure 2
Stimulated emission protocol with number resolved $π$ pulse and hidden Markov model analysis. (a) Pulse sequence for stimulated emission includes cavity initialization in a Fock state, followed by three conditional checks to ensure the cavity did not accidentally start in $| n + 1 ⟩$ state. The next part involves a cavity displacement drive to mimic an interaction with DM, and repeated conditional qubit measurements to detect the cavity in $| n + 1 ⟩$ state. (b) Examples showing two measured qubit readout sequences for a cavity initialized in $| n ⟩ = 1$ Fock state followed by a small displacement drive $α$ . The left panel corresponds to no change in the cavity state after the DM drive as inferred by the absence of successful flips of the qubit state which results in a very small probability $P (n = 2)$ that the cavity was in the $| n = 2 ⟩$ Fock state. The right panel corresponds to an emission event where the cavity state changed from $| 1 ⟩ \to | 2 ⟩$ , resulting in multiple successful flips of the qubit state. Even with a potential readout error in the 5th measurement, the HMM analysis of this sequence of flips then indicates a very high likelihood ratio to be in $| n = 2 ⟩$ Fock state. We observe an exponential suppression of the detector-error induced false positive probability with only linear increase in the number of repeated measurements.
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Figure 3
Stimulated emission enhancement. Mean number of measured photons (positive events) as a function of the mean number of injected photons in the cavity. We initialize the cavity in a Fock state $| n ⟩$ , apply a variable displacement, perform 30 repeated qubit measurements, and analyze the measurement sequence using the HMM technique. We choose a detection threshold ( $λ_{thresh} = 10^{3}$ ) such that the detector errors are subdominant to the residual photon ( $n_{b}^{c} = 6 \times 10^{- 3}$ ) induced false positives, $λ_{thresh} > 1 / n_{b}^{c}$ [18] and subtract background detections when no displacement ( $α = 0$ ) is applied. The monotonic decrease in the detector efficiency is attributed to higher decay probability and demolition probability at higher photon number (see Supplemental Material [30], Fig. S9 which includes Ref. [49]). Anomalous behavior in $| 3 ⟩$ is attributed to the state decaying to nearby modes in the band structure formed by multiple modes of the cavity, qubit, and readout, which are close in the energy level $| q, s, r ⟩$ . For a particular displacement, more photons are detected for increasing photon number of the initial Fock state prepared. This is a clear signature of stimulated emission with an enhancement of $η_{4} (4 + 1) / η_{0} (0 + 1) = 2.78$ when the cavity is prepared in $| n = 4 ⟩$ as compared to $| n = 0 ⟩$ .
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Figure 4
Measured background counts for different Fock states in the cavity as a function of dwell time. There is no clear trend in the number of observed background counts indicating systematic effects which could be due to the state preparation steps. The error bars are plotted as $\sqrt{Counts}$ with $N_{trials} \sim 20 000$ for each point.
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Figure 5
Exclusion of dark photon parameter space with stimulated emission. Shaded regions in the dark photon parameter space [7, 51] of coupling ( $ε$ ) and mass ( $m_{γ}$ ) are excluded. In the orange band, dark photon is naturally produced in models of high scale cosmic inflation [8]. The exclusion set with stimulated emission based dark photon search is shown in the blue and red curves. On resonance with the storage cavity ( $m_{γ^{'}} c^{2} = ℏ ω_{s}$ ), the dark photon kinetic mixing angle is constrained to $ε \leq 4.24 \times 10^{- 13}$ with 90% confidence. (Inset) The horizontal extent of the excluded region is set by the bandwidth of the number resolved qubit $π$ pulse which is insensitive to any drive outside the band. The vertical limit is set by the maximum $ε$ which would result in dark photon rate greater than the value which would degrade the fidelity of Fock state preparation significantly (See Supplemental Material [30], Fig. S12). The blue shaded region represents the exclusion with the stimulated emission experiment.
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