Inverted Harmonic Oscillator Quantum Probing

---
name: inverted-harmonic-oscillator-quantum-probing
description: "Experimental probing of inverted harmonic oscillator quantum dynamics using ultracold atoms. Use when studying unstable quantum dynamics, quantum squeezing, time-reversal coherence, Wigner function tomography, or quantum simulation of inflationary field dynamics."
metadata:
  arxiv_id: "2606.05125"
  published: "2026-06-03"
  category: "quantum-physics"
---

# Inverted Harmonic Oscillator Quantum Probing

## Context

When a quantum system passes through an unstable fixed point, the local dynamics reduces to the inverted harmonic oscillator (IHO). This produces exponentially amplified macroscopic quantum states from microscopic zero-point fluctuations.

## Core Methodology

### 1. IHO Realization with Bose-Einstein Condensates
- Use AtomChip-based Bose-Einstein condensate as the quantum platform
- Radio-frequency dressing flips transverse harmonic confinement into IHO potential
- This creates an unstable fixed point where quantum fluctuations are exponentially amplified

### 2. Phase-Space Tomography
- Follow the full Wigner function of the evolving quantum state
- Reconstruct quantum state in phase space through tomographic measurements
- Track both amplification and squeezing quadratures simultaneously

### 3. Squeezing Measurement
- Observe sub-vacuum squeezing levels (demonstrated: 10.6(1.3) dB)
- Squeezing occurs in one quadrature while amplification occurs in the orthogonal quadrature
- Key metric: squeezing depth below vacuum level

### 4. Time-Reversal Coherence Certification
- Test coherent reversibility by time-reversing the IHO evolution
- Matter-wave interference between daughter clouds confirms quantum coherence
- Coherence persists over timescales far beyond initial expansion

### 5. Applications
- Force sensing with time-reversal-based coherence certification
- Analog studies of quantum fluctuation amplification in inflationary field dynamics
- Clean, controlled many-body platform for unstable quantum dynamics

## Key Results

| Metric | Value |
|--------|-------|
| Squeezing depth | 10.6(1.3) dB below vacuum |
| Platform | Bose-Einstein condensate on AtomChip |
| Coherence | Confirmed via matter-wave interference |
| Reversibility | Time-reversal of IHO evolution demonstrated |

## Pitfalls

- **Thermal noise**: BEC must be sufficiently cold to observe quantum effects above thermal background
- **RF dressing calibration**: Precise RF frequency and amplitude control needed to create accurate IHO potential
- **Tomography overhead**: Full Wigner function reconstruction requires many measurement settings
- **Decoherence timescales**: Must complete measurements before environmental decoherence destroys quantum state

## Verification

- Verify squeezing below vacuum level using calibrated homodyne detection
- Confirm time-reversal fidelity by comparing initial and final states
- Validate Wigner function negativity as signature of non-classical state

## Activation Keywords

- inverted harmonic oscillator, quantum squeezing, time-reversal coherence, Wigner tomography, Bose-Einstein condensate, AtomChip, quantum fluctuations, inflationary dynamics, 2606.05125