Optical Quantum Clocks

At the heart of any atomic clock are two quantum states in an atom or ion, which have an energy difference that is well-defined (typ. associated with long lifetimes of the involved quantum states) and that is minimally effected by the environment. The transition between these states is called „clock transition“, can be investigated spectroscopically, and serves as reference for a „local oscillator“ or „flywheel“. The local oscillator (laser or microwave, depending on the transition energy) is frequency-stabilized to the clock transition and provides stable oscillating electromagnetic radiation: This is called atomic frequency standard. Counting the oscillations of the frequency standard (e.g. one “tick” corresponds to one cycle of that oscillation) one can then realize an atomic time standard.

Traditional microwave atomic clocks rely on microwave transitions in cesium (Cs) or rubidium (Rb). Cs is actually used to define time itself: „One second is the time it takes for a 9,192,631,770 oscillations of a frequency standard stabilized to the transition between the two mF=0 hyperfine ground states of 133Cs.“. While microwave atomic clocks have served us well, their fundamental limitation lies in the relatively low frequency of the reference transition and the impact of environment-induced perturbations.

Optical atomic clocks instead use transitions in the optical domain at much higher frequencies of several 10¹⁴ Hz. Typical versions use thermal atoms (e.g. two-photon Rb clocks or high resolution spectroscopy of iodine) and have similar limits like another type of clocks that use microwave transitions in laser-cooled and trapped atoms or ions. We refer to the latter ones as „microwave quantum clocks“ due to the use of quantum technologies for laser-cooling and trapping. Both of these clock types reach relative uncertainties  of 10^-14 to (rarely) below 10^-15 (in case of Cs atomic fountain clocks).

The most advanced clocks and in terms of uncertainty and accuracy are „optical quantum clocks“. They combine laser-cooling and trapping of atoms or ions (hence quantum technologies) with optical clock transitions. The result is a vastly improved uncertainty down to 10^-18 and below. Careful analyses of environmental influences, potential errors, and corrections allow for relative accuracies on the order of 10^-18.

The two leading architectures of are: optical lattice clocks with neutral atoms and optical clocks with trapped ions.

In an optical lattice clock, thousands or tens of thousands of neutral atoms (e.g. strontium, ytterbium, mercury, cadmium, mercury, magnesium, thulium) are first laser-cooled to ultra-low temperatures. Then, they are trapped in a periodic potential created by interfering laser beams, the „optical lattice“ (Atom laser cooling and trapping), at a “magic wavelength” such that the trapping light shifts the two clock states equally and does not perturb the clock transition. The clock transition with sub-Hertz-linewidth is probed spectroscopically with the clock laser. Since many („N“) atoms are interrogated in parallel, the statistical signal-to-noise, which scales with N^-1/2, is improved and pushing down the uncertainty, which also scales with the averaging time t like t^-1/2, rapidly.

Most optical trapped-ion clocks are realized in the following way. Atoms are photo-ionized with lasers and usually one of the resulting ions is confined by rf fields while being laser-cooled to near its motional ground state. A clock laser is then frequency stabilized to the narrow sub-Hertz optical transition of this clock ion (Yb+, Sr+, Ca+, Al+, In+, Lu+, and others). Compared to optical lattice clocks, using only one ion comes with a reduced signal-to-noise and consequently the uncertainty (proportional to N^-1/2×t^-1/2) improves much slower but can also reach values on the order of 10^-18 for long averaging times. On the positive side, ions can be trapped stronger and longer than atoms, have zero or lower interaction-induced shifts, and systematic effects can often be quantified more reliably. Latest publications report on systematic uncertainties (accuracies) of optical trapped-ion clocks in the region of a few ×10⁻¹⁹.

Some special trapped-ion clock versions are

• Al⁺ clock, because Al⁺ can be hardly laser-cooled. Hence, a second ion (Ca⁺ or Mg⁺) is co-trapped together with the single Al⁺ clock ion and used for sympathetic laser-cooling as well as quantum logic detection of the Al⁺ clock ion.
• Ion clocks that use not only one but several clock ions (e.g. Sr⁺, In⁺, Ca⁺) to improve the signal to noise ratio and hence promise faster averaging down to low uncertainty values. Note, the use of x-times more ions leads to x-times faster averaging down.
• A Lu⁺ ion clock is expected to work well also with many ions and not only with a few ions due to a favorable combination of atomic properties.
• Multi-charged ions are just starting to enter the field but promise outstanding performance (e.g. low systematic effects) and scientific relevance (e.g. for studying fundamental physical like pontential time variation of the fine structure constant).

Recently, it was demonstrated that an optical clock transition can be excited in the nucleus of the thorium isotope 229Th by irradiating it with a 148 nm laser. The lifetime of the nuclear excitation is > 600 s, is expected to come with extremely low sensitivity to external perturbations, and promises outstanding scientific importance, not only for clocks in general but also for testing fundamental physics. (We did it !)

All optical quantum clocks rely on ultra-stable clock laser systems: a clock laser that probes the narrow atomic or ionic transition must have extremely low phase noise, narrow linewidth (Hz or sub-Hz), and long coherence. In addition, tunable diode laser systems cover the many wavelengths required for cooling, trapping, repumping, lattice formation, state preparation, ionizaion, and detection, and are essential in operating optical clocks. Optical frequency combs link the clock laser frequency (optical freqeuncy standard) to microwave signals and enable accurate counting of cycles e.g. to deliver well-defined pulses per second.   

From a practical standpoint, integrating such lasers in industrial 19-inch rack formats (rather than sprawling optical table setups) offers major advantages: compactness, robustness, easier deployment in non-lab environments, maintainability, and compatibility with other quantum sensing hardware.

In an optical lattice clock, thousands or tens of thousands of neutral atoms (e.g. strontium, ytterbium, mercury, cadmium, mercury, magnesium, thulium) are first laser-cooled to ultra-low temperatures. Then, they are trapped in a periodic potential created by interfering laser beams, the „optical lattice“ (Atom laser cooling and trapping), at a “magic wavelength” such that the trapping light shifts the two clock states equally and does not perturb the clock transition. The clock transition with sub-Hertz-linewidth is probed spectroscopically with the clock laser. Since many („N“) atoms are interrogated in parallel, the statistical signal-to-noise, which scales with N^-1/2, is improved and pushing down the uncertainty, which also scales with the averaging time t like t^-1/2, rapidly.