Long-lived metastable states in the 4f$^{13}$5d6s configuration of Yb$^+$

This paper reports the experimental preparation and measurement of long-lived metastable states in the 4f$^{13}$5d6s configuration of a single trapped Yb$^+$ ion, revealing lifetimes ranging from 0.92 s to over 30 s that are corroborated by atomic structure calculations and offer new prospects for quantum information and optical clock applications.

The Gist

Imagine you have a tiny, glowing marble (an atom) floating in a vacuum chamber. Usually, when you shine a light on it, it jumps up to a higher energy level and then immediately falls back down, flashing a light as it returns to its resting spot. This happens in a blink of an eye.

But what if you could push that marble into a "hidden room" where it gets stuck for a while? It's not quite asleep (ground state), but it's not fully awake (excited state) either. It's in a metastable state—a cozy, long-lasting limbo.

This paper is about finding and timing exactly how long these "hidden rooms" last in a specific type of atom called Ytterbium (Yb+).

The Experiment: A Two-Marble Dance

The scientists didn't just look at one marble; they trapped two Ytterbium ions (charged atoms) in a magnetic cage called a "Paul trap."

1. The Spectroscopy Ion (The Actor): This is the main character. The scientists hit it with a specific laser (377.5 nm, a deep violet color) to kick it out of its normal state and into one of these mysterious "hidden rooms" (the 4f135d6s configuration).
2. The Control Ion (The Watchdog): The second ion stays in the "fluorescence cycle." It keeps blinking brightly like a lighthouse. Its job is to act as a thermometer and a timer. Because the two ions are close, they cool each other down (like two people huddling for warmth). As long as the "Actor" is stuck in the dark hidden room, the "Watchdog" keeps the whole system cold and stable.

How they timed the escape:
The scientists watched the "Watchdog." As soon as the "Actor" finally gave up and fell out of its hidden room back into the normal cycle, it would start glowing again. The moment the "Actor" started glowing, the scientists knew exactly how long it had been stuck.

The Discovery: Three Different "Waiting Rooms"

The team found that the atoms didn't just get stuck for one specific amount of time. They found three different types of hidden rooms, each with a different "stay duration":

1. The Short Wait (The Coffee Break): About 0.9 seconds. This is the most common exit. The atom gets stuck for just under a second before popping back out.
2. The Long Wait (The Nap): About 10 seconds. This happened less often, but the atoms stayed stuck for a full ten seconds.
3. The Super Long Wait (The Hibernation): The scientists saw hints that some atoms stayed stuck for more than 30 seconds. They couldn't measure the exact time because their experiment had to stop after 30 seconds (to avoid the atoms bumping into stray gas molecules), but they know the door was still locked!

Why is this hard? (The "Dark" Problem)

Usually, scientists can't see an atom if it's in a metastable state; it goes "dark." If you only had one atom, and it went dark, you wouldn't know if it was stuck in a hidden room or if it had just flown away or died.

By using the second ion (the Watchdog), they solved this. The Watchdog kept the system cold and visible. If the Watchdog was still blinking, they knew the Actor was still there, just invisible. It's like having a friend hold your hand in a dark room; you know your friend is still there even if you can't see them.

What did they find inside? (The Map)

Using powerful computer simulations (like a super-advanced GPS for atoms), they figured out which specific "rooms" these atoms were visiting.

• The 0.9-second wait corresponds to a specific room called 3[3/2]o 5/2.
• The 10-second and 30-second waits likely correspond to even more complex rooms with high angular momentum (think of them as spinning very fast, which makes it harder for the atom to stop and fall back down).

Why should you care? (The Superpowers)

Why do we care about atoms getting stuck for a few seconds?

1. Better Quantum Computers: In quantum computing, information is stored in "qubits." To read the information, you need to check if the qubit is in state A or state B. If the atom is stuck in a long-lived metastable state, it's like a "shelf" where you can park the information safely while you do other calculations. The longer the shelf stays stable, the more complex the calculations you can do.
2. Super-Accurate Clocks: The most accurate clocks in the world use atoms. The longer an atom stays in a specific state without wobbling, the more precise the "tick" of the clock can be. These new, longer-lived states could lead to clocks so accurate they wouldn't lose a second in the age of the universe.
3. New Types of Memory: The paper suggests these states could be used to build "qudits" (quantum digits with more than just 0 and 1). Imagine a light switch that can be "off," "on," or "dim." These long-lived states give us more "dim" settings to work with.

The Bottom Line

The scientists successfully pushed Ytterbium atoms into a new, previously unexplored "limbo" state. They proved these atoms can stay there for nearly a minute, which is an eternity in the quantum world. This discovery opens the door to faster quantum computers and clocks that are even more precise than anything we have today.

Technical Summary

Here is a detailed technical summary of the paper "Long-lived metastable states in the 4f¹³5d6s configuration of Yb⁺".

1. Problem Statement

Trapped ions, particularly $^{171}\text{Yb}^+$, are leading candidates for quantum computing and optical atomic clocks. However, current implementations face limitations regarding metastable states:

• Short-lived states: The widely used $^2D_{3/2}$ and $^2D_{5/2}$ states have lifetimes of $\sim$50 ms and $\sim$7 ms, respectively, which are too short for certain qubit manipulation and clock applications.
• Ultra-long-lived states: The $^4F^o_{7/2}$ state has a lifetime of $\sim$1.6 years, but its coupling to the ground state is via an extremely weak electric octupole (E3) transition, making it difficult to use for quantum logic operations.
• The Gap: There is a need for metastable states with intermediate lifetimes (seconds) and stronger coupling strengths to facilitate efficient state detection (electron shelving) and qubit/qudit operations.

Theoretical calculations predicted the existence of such states within the $4f^{13}5d6s$electron configuration of Yb$^+$, specifically states with angular momentum$j > 7/2$ where electric dipole (E1) decay is forbidden. However, these states had never been experimentally observed or their lifetimes measured.

2. Methodology

The authors employed a dual-ion trapped ion system to prepare, manipulate, and detect these metastable states.

• Experimental Setup:
  • Two $^{174}\text{Yb}^+$ ions were trapped in a microfabricated 3D linear Paul trap.
  • Spectroscopy Ion: The ion of interest, prepared in the $^4F^o_{7/2}$ state.
  • Control Ion: A co-trapped ion used for sympathetic cooling and fluorescence detection.
• State Preparation Sequence:
  1. Initialization: Both ions were optically pumped into the long-lived $^4F^o_{7/2}$ state using a 411 nm laser.
  2. Excitation: The spectroscopy ion was driven on the $^4F^o_{7/2} \to (7/2, 0)_{7/2}$ electric dipole (E1) transition at 377.5 nm for 50 ms. This populates the $4f^{13}5d6s$ configuration.
  3. Decay & Waiting: The ion was allowed to decay into various metastable states.
  4. Clearing: A 760 nm laser was used to clear the $^4F^o_{7/2}$ state of the control ion (returning it to the cooling cycle) while leaving the spectroscopy ion in its metastable state.
  5. Detection: The system monitored the fluorescence of the control ion. If the spectroscopy ion decayed back into the cooling cycle ($^2S_{1/2}$ or $^2D_{3/2}$), it would start fluorescing, and the "return time" was recorded.
• Variations: Experiments were run with the 760 nm "clear" laser either ON or OFF during the wait time to distinguish decay paths that return directly to $^4F^o_{7/2}$ versus those that decay to $^2D$ states.
• Theoretical Support: Atomic structure calculations were performed using the AMBiT package (Configuration Interaction + Many-Body Perturbation Theory) to predict lifetimes and decay channels.

3. Key Contributions

• First Experimental Observation: This is the first experimental demonstration of long-lived metastable states in the $4f^{13}5d6s$configuration of Yb$^+$.
• Lifetime Measurement: The authors measured lifetimes on the scale of seconds, a regime previously unexplored for these specific configurations.
• State Identification: They qualitatively identified the specific quantum states responsible for the observed decay signals by correlating experimental data with theoretical predictions.
• Validation of Theory: The results corroborate previous theoretical calculations (e.g., by Fawcett and Wilson) and provide new benchmarks for atomic structure models involving complex open-shell configurations.

4. Results

The experiment recorded the cumulative probability of the spectroscopy ion remaining "dark" (metastable) over a 30-second window. The data revealed three distinct decay components:

1. Dominant Decay ($\tau_1$):

   • Measured Lifetime: $0.92(8)$ s.
   • Identification: Assigned to the $^3[3/2]^o_{5/2}$ state (energy $\approx$ 3.32 eV).
   • Mechanism: Decay is driven by configuration interaction (CI) allowing E1 transitions to the $^2D$ states. The authors calculated a branching fraction of $\sim$71% to the $^2D_{5/2}$ state.
   • Theoretical Match: AMBiT calculations predicted a lifetime of 3.1 s, while previous theory predicted 5.2 s. The experimental value is within the same order of magnitude, confirming the state's identity.

2. Weaker Decay ($\tau_2$):

   • Measured Lifetime: $9.8(+2.9, -2.0)$ s.
   • Identification: Likely attributed to the $^3[7/2]^o_{9/2}$ state (energy $\approx$ 4.10 eV).
   • Mechanism: This state cannot decay via E1 to $^2D$ states due to selection rules. It likely decays via Magnetic Dipole (M1) transitions to lower $4f^{13}5d6s$ states, followed by E1 decay.
   • Theoretical Match: Recent theoretical work estimated an M1-limited lifetime of $\sim$9.9 s, matching the observation.

3. Long-lived Component ($\tau_3$):

   • Observation: Evidence of a lifetime $> 30$ s.
   • Identification: Plausibly attributed to the $^3[11/2]^o_{9/2}$ state (energy $\approx$ 3.75 eV).
   • Constraint: The exact lifetime could not be measured precisely because it exceeds the background gas collision rate (Langevin collisions) in the vacuum chamber, which limits the observation window.

Control Measurements:

• Control experiments varying laser powers (370 nm and 935 nm) confirmed that off-resonant scattering did not significantly alter the measured lifetimes.
• Background gas collision rates were measured to be $\sim$1/43 s, confirming that the observed $>30$ s lifetimes are intrinsic to the ions and not limited by vacuum quality.

5. Significance and Applications

The discovery of these intermediate-lifetime states offers significant advantages for quantum technology:

• Improved Qubit State Detection: The $^3[3/2]^o_{5/2}$ state (0.92 s lifetime) provides an attractive alternative for "electron shelving" in qubit readout. It offers a faster return time than the $^4F^o_{7/2}$ state (years) while being significantly longer-lived than the $^2D$ states (ms), allowing for more robust and faster state discrimination.
• Qudit Operations: For qudit-based quantum computing (using isotopes like $^{173}\text{Yb}^+$), these states enable efficient shelving operations required for reading out high-dimensional quantum states.
• Optical Clocks: These states could serve as new candidates for optical clock transitions, potentially offering different systematic shift properties compared to current standards.
• Fundamental Physics: The ability to access and measure these complex configurations aids in testing atomic structure theories and searching for physics beyond the Standard Model (e.g., via isotope shift measurements).

In conclusion, this work bridges the gap between short-lived and ultra-long-lived metastable states in Yb$^+$, opening new avenues for high-fidelity quantum information processing and precision metrology.