A cryogenic Paul trap for probing the nuclear isomeric excited state $^{229\text{m}}$Th$^{3+}$

This paper presents the design, construction, and successful commissioning of a cryogenic Paul trap at LMU Munich that enables the extraction, purification, and sympathetic laser cooling of $^{229\text{m}}$Th$^{3+}$ ions alongside $^{88}$Sr$^{+}$ ions, forming mixed-species Coulomb crystals to facilitate future laser excitation of the nuclear isomeric transition.

The Gist

The Atomic Stopwatch: Catching a Ghostly Nucleus in a Cryogenic Cage

Imagine you are trying to build the most precise clock in the universe. Not a clock with gears or springs, but one based on the heartbeat of an atom's nucleus. This is the goal of the scientists at LMU Munich, and they have just built a brand-new, high-tech "cage" to catch and hold a very special, very shy particle: a Thorium ion.

Here is the story of their new machine, explained without the heavy jargon.

1. The Goal: A Nuclear "Super-Clock"

Most clocks tick by counting the vibrations of electrons orbiting an atom. But the scientists want to use the nucleus (the center of the atom) instead.

• The Analogy: Think of an electron as a dancer spinning wildly on a stage. It's easily distracted by wind, music, or people bumping into it. The nucleus, however, is like a rock sitting in the center of the stage. It barely moves and is almost impossible to disturb.
• The Prize: If they can make a clock based on this "nuclear rock," it will be so precise it could detect things we can't see now, like dark matter or changes in the fundamental laws of physics. The specific "rock" they are using is a Thorium atom in a special excited state (called 229mTh).

2. The Problem: The Shy Ghost

The problem is that this Thorium nucleus is incredibly fragile.

• The Analogy: Imagine trying to photograph a ghost. If you shine a bright light on it, or if the room is too hot, or if the air is too dusty, the ghost vanishes or gets distorted.
• The Challenge: To study this nucleus, they need to trap a single Thorium ion in a vacuum so perfect it's emptier than outer space, and keep it so cold that it stops shivering. If the air is too "dusty" (too many gas molecules), the Thorium will bump into them and lose its special state.

3. The Solution: The Cryogenic Paul Trap

The team built a machine called a Cryogenic Paul Trap. Let's break down what that means using a kitchen analogy:

• The Cage (The Trap): Instead of a physical cage with bars, they use invisible electric fields. Imagine holding a marble in mid-air by blowing air from four different directions. If the marble tries to move left, the air pushes it right. This is how they hold the Thorium ion without touching it.
• The Freezer (Cryogenic): The machine is cooled down to about 8 Kelvin (that's -265°C, just a few degrees above absolute zero).
  • Why? At this temperature, any stray gas molecules in the room freeze and stick to the walls like frost on a window. This creates a "super-vacuum," ensuring the Thorium ion has nothing to bump into.
• The Bodyguard (Sympathetic Cooling): The Thorium ion is too hard to cool down directly with lasers. So, the scientists bring in a bodyguard: a Strontium ion.
  • The Analogy: Imagine the Thorium is a hot, grumpy toddler who refuses to sit still. The Strontium is a calm, well-behaved child who loves ice cream (lasers). The scientists cool the Strontium down with lasers. Because the two ions are holding hands (electrically connected), the Strontium cools the Thorium down too. They form a "Coulomb crystal"—a tiny, frozen chain of ions dancing in perfect sync.

4. The Journey: From Source to Cage

Getting the Thorium into the trap is like a high-stakes relay race through a maze:

1. The Birth: They start with a Uranium source. As Uranium decays, it spits out Thorium ions.
2. The Air Brake (Buffer Gas): These Thorium ions are flying super fast (like bullets). They are shot into a chamber filled with ultra-pure Helium gas. The gas acts like a thick fog, slowing the ions down until they are just drifting.
3. The Funnel: An "RF Funnel" (a cone of electric fields) guides these slow-moving ions through a tiny nozzle, like water through a garden hose nozzle, creating a focused beam.
4. The Bouncer (Mass Separator): The beam is messy; it contains Thorium, Uranium, and other junk. A Quadrupole Mass Separator acts like a bouncer at a club. It checks the "ID" (mass and charge) of every particle and only lets the specific Thorium ions (and later, the Strontium bodyguards) pass.
5. The Destination: The purified ions are shot into the frozen trap, where they are caught by the electric fields and cooled by the Strontium.

5. The Results: A Successful Catch

The paper reports that the machine works perfectly.

• They successfully caught the Thorium ions.
• They successfully cooled them down using the Strontium "bodyguards."
• They formed a Coulomb Crystal, a tiny, visible chain of ions that looks like a string of pearls under a microscope.
• They proved the vacuum is so good that the ions can stay trapped for days without bumping into anything.

Why Does This Matter?

This machine is the prototype for the world's first Nuclear Clock.

• Current Clocks: Our best atomic clocks are amazing, but they might lose a second over billions of years.
• The Future: This Thorium nuclear clock could be so precise that it wouldn't lose a second even if the universe was billions of years old. It could help us navigate space with perfect accuracy, map the Earth's gravity from space, or even prove Einstein's theories of relativity in new ways.

In short: The scientists built a super-cold, super-clean, electric cage to catch a ghostly nuclear particle, calm it down with a laser-cooled bodyguard, and prepare it to become the most accurate timekeeper humanity has ever created.

Technical Summary

1. Problem Statement

The nuclear isomeric state of Thorium-229 ($^{229m}\text{Th}$) possesses the lowest known excitation energy (~8.4 eV), making it a unique candidate for a "nuclear clock" with potential precision surpassing current optical atomic clocks. While recent breakthroughs have achieved laser excitation of $^{229m}\text{Th}$ embedded in solid-state crystals (e.g., CaF$_2$, MgF$_2$), these environments introduce systematic uncertainties due to crystal field effects and refractive index scaling.

To realize a high-precision nuclear clock and accurately determine the radiative lifetime of the isomer, spectroscopy must be performed on trapped, isolated ions in an ultra-high vacuum (UHV). However, this presents significant challenges:

• Lifetime Requirements: Theoretical predictions suggest a radiative lifetime of $\sim 10^3$ seconds. Measuring this requires ion storage times of many hours in an environment free of background gas collisions.
• Ion Source & Purity: Generating pure $^{229m}\text{Th}^{3+}$ ions from a $^{233}\text{U}$ source requires efficient extraction from a buffer gas and rigorous mass/charge separation to remove daughter products and contaminants.
• Thermal Management: To achieve the necessary UHV ($<10^{-8}$ mbar) and suppress thermal noise, the trap must operate at cryogenic temperatures (~8 K), necessitating vibration isolation to prevent heating of the trapped ions.
• Cooling: $^{229m}\text{Th}^{3+}$ lacks suitable direct cooling transitions; it must be sympathetically cooled by a co-trapped, laser-coolable ion species (e.g., $^{88}\text{Sr}^+$).

2. Methodology and Experimental Setup

The authors designed, built, and commissioned a comprehensive cryogenic experimental platform at LMU Munich. The system consists of a horizontal ion beam line connecting several key components:

• Ion Source (Buffer-Gas Stopping Cell):
  • A $^{233}\text{U}$ source (10 kBq) emits recoil $^{229(m)}\text{Th}$ ions (up to 84 keV).
  • Ions are thermalized in ultra-pure Helium gas (32 mbar) within a compact stopping cell.
  • Extraction is achieved via a conical RF-DC funnel and a de Laval nozzle, creating a supersonic gas jet that drags ions into the next stage.
• Ion Manipulation & Purification:
  • Extraction RFQ: A segmented radio-frequency quadrupole cools and bunches the extracted ions.
  • Ion Guide: A second RFQ guides ions and serves as a catcher for laser-ablated $^{88}\text{Sr}^+$ ions (from a SrTiO$_3$ target).
  • Quadrupole Mass Separators (QMS): Two QMS units (QMS 1 and QMS 2) provide high-resolution mass filtering ($R \approx 150$). They separate $^{229}\text{Th}^{3+}$ from $^{233}\text{U}$, daughter products, and other strontium isotopes. The system utilizes active PID feedback loops to stabilize RF/DC voltages for precise mass selection.
• Cryogenic Linear Paul Trap:
  • Environment: The trap operates at ~8 K inside nested copper heat shields (4 K and 40 K stages) cooled by a pulse-tube cryocooler.
  • Vibration Isolation: A specialized helium-filled interface (ULV interface) decouples the cryocooler vibrations from the trap, achieving residual amplitudes $<10$ nm at frequencies $>60$ Hz.
  • Optical Access: The setup features multiple viewports and pocket-shaped apertures for laser cooling, spectroscopy, and fluorescence detection (EM-CCD) at 422 nm ($^{88}\text{Sr}^+$) and 690 nm ($^{229(m)}\text{Th}^{3+}$).
• Sympathetic Cooling:
  • $^{88}\text{Sr}^+$ ions are laser-cooled using 422 nm and 1092 nm transitions.
  • These ions form a Coulomb crystal that sympathetically cools the $^{229(m)}\text{Th}^{3+}$ ions via Coulomb interaction, allowing for the formation of mixed-species crystals.

3. Key Contributions

• First Cryogenic Trap for $^{229m}\text{Th}^{3+}$: This is the first dedicated cryogenic Paul trap setup designed specifically for the extraction, purification, and trapping of $^{229m}\text{Th}^{3+}$ ions from a buffer-gas cell.
• High-Efficiency Extraction: Demonstrated a buffer-gas cell extraction efficiency of >4%, yielding ~200 ions/second, with a compact design optimized for the specific recoil energies of the thorium source.
• Advanced Mass Filtering: Successfully implemented a dual-QMS system with active voltage stabilization to isolate $^{229}\text{Th}^{3+}$ from complex decay chains and ablation contaminants with high resolution.
• Mixed-Species Coulomb Crystals: Achieved the stable trapping and sympathetic cooling of $^{229(m)}\text{Th}^{3+}$ ions within a lattice of laser-cooled $^{88}\text{Sr}^+$ ions, visualized as mixed-species Coulomb crystals.
• Vacuum Characterization: Validated the ultra-high vacuum conditions required for long-term storage by monitoring ion loss rates.

4. Key Results

• Ion Extraction & Transport: The system successfully extracted $^{229(m)}\text{Th}^{3+}$ from the buffer-gas cell, transported it through 1.4 m of beam line, and purified it using the QMS. Mass spectra confirmed the separation of $^{229}\text{Th}^{3+}$ from $^{233}\text{U}$ and other contaminants.
• Coulomb Crystal Formation: The team successfully created mixed-species Coulomb crystals containing both $^{88}\text{Sr}^+$ and $^{229(m)}\text{Th}^{3+}$.
  • $^{88}\text{Sr}^+$ ions were cooled to form a crystal.
  • $^{229(m)}\text{Th}^{3+}$ ions were injected and sympathetically cooled, appearing as "dark spots" in the fluorescence image of the strontium crystal.
  • SIMION simulations confirmed the positions and shapes of the ions within the crystal, validating the trapping potential models.
• Vacuum Performance:
  • Based on the storage time of $^{88}\text{Sr}^+$ ions (observed for 8 days with only chemical reaction losses, not ion loss), a lower limit for the storage time of $\tau \approx 192$ hours was established.
  • Using the Langevin collision model, the partial pressure of residual hydrogen was estimated to be $p_{H_2} \approx 1.07 \times 10^{-15}$ mbar at 8 K. This confirms the environment is suitable for measuring the radiative lifetime of the isomer.
• Vibration Suppression: The ULV interface successfully reduced vibrations transmitted to the laser table by two orders of magnitude, ensuring the stability required for precision spectroscopy.

5. Significance

This work establishes the experimental backbone for the "ThoriumNuclearClock" project. By demonstrating the ability to trap, purify, and sympathetically cool $^{229m}\text{Th}^{3+}$ ions in a cryogenic, ultra-high vacuum environment, the authors have removed the primary technical barriers to:

1. Measuring the Radiative Lifetime: Determining the intrinsic lifetime of $^{229m}\text{Th}$ in vacuum without the perturbations of solid-state hosts.
2. Nuclear Clock Development: Providing the platform necessary for direct VUV excitation of the nuclear transition, which is the critical step toward building a nuclear clock with a projected systematic uncertainty of $1.5 \times 10^{-19}$.
3. Fundamental Physics: Enabling high-precision tests of fundamental physics, including the search for variations in the fine-structure constant ($\alpha$) and ultra-light dark matter candidates.

The successful commissioning of this setup marks a transition from solid-state spectroscopy to the ultimate goal of trapped-ion nuclear spectroscopy, paving the way for the next generation of frequency standards.