[Paper Review] Adiabatic cooling of a single trapped ion

G. Poulsen, Michael Drewsen|arXiv (Cornell University)|Oct 16, 2012

Cold Atom Physics and Bose-Einstein Condensates1 references3 citations

TL;DR

This paper demonstrates adiabatic cooling of a single ⁴⁰Ca⁺ ion in a linear radiofrequency trap by slowly reducing the axial secular frequency from 583 kHz to 75 kHz. The method cools the ion from an initial Doppler temperature of 0.65 mK to 87 μK, with near-perfect adiabatic behavior confirmed by temperature and ground state population measurements, showing promise for quantum information and ultracold chemistry.

ABSTRACT

We present experimental results on adiabatic cooling of a single 40Ca+ ion in a linear radiofrequency trap. After a period of laser cooling, the secular frequency along the rf-field-free axis is adiabatically lowered by nearly a factor of eight from 583 kHz to 75 kHz. For an ion originally Doppler laser cooled to a temperature of 0.65 +/- 0.03 mK, a temperature of 87 +/- 7 μK is measured after the adiabatic expansion. Applying the same adiabatic cooling procedure to a single sideband cooled ion in the ground state (P0 = 0.978 +/- 0.002) resulted in a final ground state occupation of 0.947 +/- 0.005. Both results are in excellent agreement with an essentially fully adiabatic behavior. The results have a wide range of perspectives within such diverse fields as ion based quantum information science, high resolution molecular ion spectroscopy and ion chemistry at ultra-low temperatures.

Motivation & Objective

• To experimentally demonstrate pure adiabatic cooling of a single trapped ion, a regime not previously explored.
• To investigate the feasibility of achieving ultra-low temperatures in a single ion system using adiabatic expansion of the trap potential.
• To assess the preservation of motional ground state population during adiabatic cooling for quantum information applications.
• To evaluate the performance of adiabatic cooling in reducing ion temperature below the Doppler limit.
• To explore the potential of adiabatic cooling for high-resolution spectroscopy and ultracold ion chemistry.

Proposed method

• The axial secular frequency νz was adiabatically reduced from 583 kHz to 75 kHz by slowly lowering the dc potential on the end electrodes via a filtering circuit with a 1 ms time constant.
• Laser cooling was applied first via Doppler cooling (5 ms) or sideband cooling (6 ms) at the high-frequency regime to prepare the ion in a low-temperature or ground state.
• The adiabatic condition was maintained via the criterion ẋνz / νz² ≪ 2π, ensuring the system remained in the adiabatic regime throughout the expansion.
• Ion temperature was measured by fitting the excitation probabilities of the carrier and red sidebands to a thermal distribution model.
• Ground state population was determined by comparing the excitation probabilities of the first red and blue sidebands.
• A low-power final cooling step (Rabi frequency ~30 kHz, 5 ms) was applied after high-power sideband cooling to minimize off-resonant excitation and improve ground state fidelity.

Experimental results

Research questions

• RQ1 Can adiabatic cooling be effectively applied to a single trapped ion to achieve temperatures below the Doppler limit?
• RQ2 To what extent is the motional state preserved during adiabatic expansion, particularly for an ion initially in the ground state?
• RQ3 How well does the measured final temperature scale with the secular frequency reduction, indicating adiabatic behavior?
• RQ4 What is the impact of high-power sideband cooling on the final ground state population, and how does it compare to the initial population?
• RQ5 Can adiabatic cooling be used to reach the ultracold regime (μK range) for applications in quantum information and ultracold chemistry?

Key findings

• The ion temperature was reduced from an initial 0.65 ± 0.03 mK after Doppler cooling to 87 ± 7 μK after adiabatic expansion, corresponding to a cooling factor of approximately 7.8.
• The final temperature ratio closely matched the inverse ratio of the secular frequencies (583 kHz / 75 kHz ≈ 7.8), confirming near-ideal adiabatic behavior.
• For a sideband-cooled ion initially in the ground state with population P₀ = 0.978 ± 0.002, the final ground state population was measured as 0.947 ± 0.005, indicating minimal heating during expansion.
• The final state distribution corresponds to a translational temperature of approximately 1.3 μK, consistent with the measured ground state population.
• The adiabatic cooling process preserved quantum state fidelity with minimal spurious heating, as evidenced by consistent heating rates of one vibrational quantum per second in the 280–585 kHz range.
• The results demonstrate that adiabatic cooling is a viable method for reaching the μK regime in single-ion systems, enabling applications in quantum information and ultracold chemistry.