Testing Supersymmetric Hidden Sectors with Long-Baseline Atom Interferometers

This paper proposes that long-baseline atom interferometers like MAGIS and AION can serve as sensitive non-collider probes for supersymmetric hidden sectors by detecting coherent phase oscillations induced by ultralight moduli or hidden scalars, thereby mapping these signals to fundamental parameters of supersymmetric and string-motivated theories.

The Gist

Imagine the universe is filled with invisible, ultra-light "ghosts" called hidden sectors. In the world of high-energy physics, these are often linked to theories like Supersymmetry (SUSY) or String Theory. Usually, to find these ghosts, scientists build massive machines like the Large Hadron Collider (LHC) to smash particles together at high speeds, hoping to create these ghosts out of pure energy.

But this paper proposes a completely different way to catch them: listening for their whispers instead of waiting for a shout.

The Experiment: A Quantum Ruler

The paper focuses on giant, futuristic experiments called MAGIS and AION. Think of these as incredibly sensitive "quantum rulers" stretching hundreds of meters long.

Instead of using mirrors (like the famous LIGO gravitational wave detectors), these experiments use clouds of atoms that are cooled down until they act like waves. Scientists shoot laser pulses at these atoms to split them, send them on different paths, and then smash them back together.

• The Analogy: Imagine two runners starting at the same time on a track. If one runner hits a tiny bump or a slight breeze that the other didn't, they will finish slightly out of sync. In these experiments, the "runners" are atoms, and the "bump" is a change in the fundamental laws of physics. When the atoms recombine, they create an interference pattern (a wave pattern). If the pattern shifts, it means something changed the atoms' "internal clock" or energy while they were flying.

The Target: The "Ghost" Fields

The paper suggests that if the universe contains these ultralight hidden fields (like moduli, dilatons, or hidden scalars), they wouldn't be static. They would be wiggling.

• The Analogy: Imagine the air in a room is filled with a very faint, invisible fog that is constantly vibrating up and down. If you have a very sensitive microphone, you might hear a hum.
• In this case, the "fog" is a field that makes the fundamental constants of nature (like the mass of an electron or the strength of forces) oscillate slightly. As the field vibrates, it makes the atoms in the experiment tick slightly faster or slower, creating a rhythmic "hum" in the quantum phase.

The Discovery: Reading the Invisible

The author, Oem Trivedi, shows that these atom interferometers can act as a decoder ring for Supersymmetry.

Usually, if we find a hidden field, we just know "something is there." But this paper explains that because these fields are tied to the deep mathematics of Supersymmetry, the way they wiggle the atoms tells us exactly which mathematical gears are turning in the hidden sector.

• The Analogy: Imagine you are in a dark room with a complex machine. You can't see the machine, but you can hear a specific rattle.
  • A standard detector might just say, "There is a rattle."
  • This paper says, "Because of how the atoms rattle, we know the rattle is coming from the gauge kinetic function (a specific mathematical part of the machine), the Yukawa coupling (another part), or the QCD scale (the glue holding things together)."

It translates the "hum" of the atoms into a map of the hidden sector's geometry. It tells us how the hidden world is connected to our visible world (electrons, protons, light) through tiny "leaks" or mixings.

Why This Matters

1. It's a New Kind of Hunt: Unlike colliders that look for heavy particles created in explosions, these experiments look for light, ancient relics that have been drifting through the universe since the Big Bang. They are too light to be made in a collider, but they are everywhere.
2. Sensitivity to the "Hidden": The paper argues that even if these hidden fields are 99.999% invisible to us, these atom experiments are sensitive enough to detect the tiny 0.001% "mixing" where they interact with our atoms.
3. The "Null" Result is Still a Win: Even if they don't find a signal, the experiment sets strict rules. It says, "If these hidden fields exist, they cannot be connected to our world in this specific mathematical way." This helps physicists rule out certain versions of Supersymmetry and String Theory.

Summary

In short, this paper proposes using giant, laser-controlled atom clouds as ultra-sensitive microphones to listen for the rhythmic vibrations of invisible, ultra-light fields predicted by advanced physics theories. If they hear a hum, they can use the pitch and volume of that hum to reverse-engineer the complex mathematical structure of the hidden universe, proving that these "ghosts" are real and telling us exactly how they interact with the matter we can see.

Technical Summary

Technical Summary: Testing Supersymmetric Hidden Sectors with Long-Baseline Atom Interferometers

Problem Statement
Current high-energy physics searches for supersymmetry (SUSY) and string-motivated hidden sectors rely heavily on collider experiments to produce heavy superpartners directly. However, many theoretical frameworks (e.g., KKLT, large volume scenarios, sequestered supergravity) predict the existence of ultralight scalar fields—such as moduli, dilatons, or hidden scalars—that remain below collider thresholds. These fields may constitute a fraction of dark matter or exist as coherent infrared relics. While atom interferometers like MAGIS and AION are primarily designed for gravitational wave detection and dark matter searches, their specific sensitivity to coherent phase shifts has not been fully mapped to the microscopic parameters of supersymmetric hidden sectors. The paper addresses the gap between the phenomenological constraints of atom interferometry and the fundamental derivatives of SUSY/SUGRA Lagrangians.

Methodology
The paper establishes a theoretical mapping between the observable signal in a long-baseline atom interferometer and the underlying geometry of a supersymmetric hidden sector.

1. Interferometric Response: The authors utilize the standard response of a light-pulse atom interferometer to acceleration and time-dependent variations in microscopic energy scales. For a long-baseline configuration (separation $L$), the differential phase shift $\Delta\Phi_{grad}$ is sensitive to tidal fields and coherent oscillations of fundamental constants.
2. Scalar Field Dynamics: Ultralight scalars ($\phi$) constituting a fraction $F_{DM}$ of the local dark matter density are modeled as classical coherent oscillators: $\phi(t) = \phi_0 \cos(m_\phi t + \beta)$. These fields induce a fractional modulation in atomic transition frequencies ($\delta\omega_A/\omega_A$).
3. SUSY/SUGRA Mapping: The core methodological contribution is deriving the "effective scalar coupling" ($d_{eff}^{SUSY}$) not as a phenomenological constant, but as a function of the derivatives of visible sector parameters with respect to the light modulus direction ($M$). Specifically, the paper relates the atomic frequency shift to:
   • Derivatives of the gauge kinetic function ($f_a$) affecting the fine-structure constant ($\alpha$).
   • Derivatives of the Kähler metrics ($Z_i$), Yukawa couplings ($y_i$), and Higgs sector parameters ($v_d$) affecting fermion masses ($m_e$).
   • Derivatives of the strong gauge kinetic function affecting the QCD scale ($\Lambda_{QCD}$).

The total effective coupling is expressed as a linear combination of these microscopic derivatives weighted by sensitivity coefficients ($K_\alpha, K_{me}, K_g$, etc.):
$$d_{eff}^{SUSY} = K_\alpha d_e + K_{me} d_{me} + K_g d_g + \dots$$

Key Contributions

• Microscopic Interpretation of Phase Signals: The paper provides the first explicit derivation linking the atom interferometric phase signal to the specific geometric derivatives of the SUSY/SUGRA potential (gauge kinetic functions, Kähler metrics, Yukawa couplings). This transforms the interferometer from a generic dark matter detector into a probe of the hidden sector's coupling geometry.
• Constraint Formulation: The authors derive a symbolic constraint equation (Eq. 45) that bounds the combination of these derivatives based on the null search for oscillatory phase signals. This constraint applies to the product of the effective coupling and the dark matter fraction ($\sqrt{F_{DM}}$).
• Benchmark Projections: The paper calculates illustrative reach for future MAGIS/AION experiments. Assuming a phase sensitivity of $10^{-8}$ rad, the experiments could probe effective couplings as small as $|d_{eff}^{SUSY}| \lesssim 5 \times 10^{-11}$ for scalar masses around $10^{-17}$ eV.
• Mixing Angle Interpretation: The work interprets these bounds in terms of a "visible sector admixture" or mixing angle ($\epsilon$), demonstrating that these instruments can detect extremely small couplings ($\epsilon \sim 10^{-9}$) between hidden ultralight fields and the Standard Model.

Results
The analysis demonstrates that long-baseline atom interferometers are sensitive to the "infrared leakage" of hidden sector geometry.

• Sensitivity Range: The proposed method is sensitive to scalar masses in the sub-Hz to Hz range ($10^{-17}$ eV to $10^{-12}$ eV), a regime inaccessible to colliders but relevant for coherent dark matter.
• Coupling Limits: For a scalar mass of $10^{-15}$ eV and assuming the scalar constitutes all local dark matter ($F_{DM}=1$), the experiments could constrain the effective coupling to $|d_{eff}^{SUSY}| \lesssim 5 \times 10^{-9}$.
• Signal Characterization: A detection would manifest as a narrow, oscillatory phase line. The frequency determines the scalar mass ($m_\phi$), while the amplitude and response across different atomic transitions could distinguish the origin of the coupling (electromagnetic, fermion mass, QCD, or Higgs sector).

Significance and Claims
The paper claims that this approach offers a non-collider probe of supersymmetric and string-motivated physics.

• Complementarity: Unlike collider searches that look for heavy superpartners, or astrophysical probes that look for gravitational imprints, atom interferometry tests the coupling structure of light hidden sectors to the visible world.
• Model Specificity: The constraints are not generic to all SUSY models but specifically target constructions where an ultralight modulus controls visible sector parameters (e.g., sequestered models, no-scale supergravity, axiverse-inspired constructions).
• Modest Scope: The authors explicitly state that these results do not rule out supersymmetry or string theory as a whole, nor do they constrain models where all moduli are heavy or completely sequestered. Instead, the method tests the specific subset of low-energy Lagrangians where an ultralight scalar exists with non-negligible abundance and sufficient coupling to produce observable atomic phase modulation.
• Future Outlook: The paper emphasizes that the provided numbers are benchmark projections. A definitive experimental limit requires incorporating the full frequency-dependent response function, environmental noise, and specific pulse sequences of the actual MAGIS/AION hardware.