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