Can Quantum Logic Techniques Be Applied to Complex Molecular Ions?

[kelly0303]

Hello! I read several papers about using quantum information techniques in order to do precision spectroscopy on ions. Usually they trap 2 ions in a quadrupole trap and the 2 ions are coupled through their vibrational motion along the trap axis. However most of these results involve atomic ions. I saw some results with molecular ions such as CaH+ or MgH+, however they are trapped together with another atomic ion, and these 2 particular molecules have quite a simple structure and a large rotational spacing. I was wondering if with the current technology it is possible to apply the same techniques to more complex molecules (diatomic or polyatomics), or are there some big challenges in that case? In principle the coupling of the motion of the 2 ions shouldn't care about how complex they are. Also, would it be possible to do the same with 2 molecular ions, instead of a molecule and an atom? For example, I came across this cool paper in which they entangle 2 atomic ions and use that to measure their relative isotope shift with very high accuracy. Would it be possible, for example, to measure the isotope shift between 2 molecular ions by using the same techniques?

NOTE: In terms of challenges, I am curious about challenges specific to this approach, not to molecules in general (i.e. not issues that appear in normal laser spectroscopy such as producing the molecules of interests in the first place). Also I am not thinking about why it would be useful to apply these techniques, I am just curious if it is possible at all.

Thank you!

 

[f95toli]

Some of the very early experimental work on quantum computing was done using molecules. The techniques for doing this are essentially based on using conventional NMR,

I don't think there is a fundamental reason for why you can't use molecules. However, I suspect the reason for why this is not a very popular approach is because there are a bunch of parameters that have be in the right range for a system to be good candidate for a QIP experiment; the most obvious being good coherence times and some "easy" way to control and read-out the system.

 

[kelly0303]

Some of the very early experimental work on quantum computing was done using molecules. The techniques for doing this are essentially based on using conventional NMR,

I don't think there is a fundamental reason for why you can't use molecules. However, I suspect the reason for why this is not a very popular approach is because there are a bunch of parameters that have be in the right range for a system to be good candidate for a QIP experiment; the most obvious being good coherence times and some "easy" way to control and read-out the system.

Thank a lot for this! For the coherence time, I guess one important factor is the lifetime of the excited level, which varies for different species. But beside that, wouldn't coherence be mainly external and so more or less the same for atoms or molecules? Or are there external noise sources that atoms might be insensitive to (e.g. BB radiation)?

 

[TeethWhitener]

Thank a lot for this! For the coherence time, I guess one important factor is the lifetime of the excited level, which varies for different species. But beside that, wouldn't coherence be mainly external and so more or less the same for atoms or molecules? Or are there external noise sources that atoms might be insensitive to (e.g. BB radiation)?

The more atoms in your system, the larger the number of degrees of freedom, and the more opportunities for internal vibrational relaxation there will be. If you're looking only to excite one intermolecular mode, it's likely that with bigger molecules, the energy in this mode will quickly redistribute to a roughly thermal distribution of lower-lying vibrational modes. Two atoms only have one vibrational degree of freedom, so they can't decohere in the same way.

 

[kelly0303]

The more atoms in your system, the larger the number of degrees of freedom, and the more opportunities for internal vibrational relaxation there will be. If you're looking only to excite one intermolecular mode, it's likely that with bigger molecules, the energy in this mode will quickly redistribute to a roughly thermal distribution of lower-lying vibrational modes. Two atoms only have one vibrational degree of freedom, so they can't decohere in the same way.

I am a bit confused. So there are 2 types of vibrations: internal ones (which happens only for molecules) and center of mass ones. The center of mass motion should be the same whether we have atoms or molecules, right (of course depending on the mass of the given particle)? In terms of internal degrees of freedom, usually you don't go to higher vibrational modes. In most of the experiments (whether precision spectroscopy, or quantum information) you work in the lowest few rotational levels, of the ground vibrational and electronic state. Are you saying that preparing a molecules in a given J would be hard due to blackbody radiation, which would lead to transitions to other J values?

 

[TeethWhitener]

I’m sorry, it sounded like you were asking why vibrational states in polyatomics are shorter-lived than in diatomics.

But even in the ground vibrational state probing rotational levels, if the molecule gets bigger, the rotational constant will decrease, and if the molecule is asymmetric, you’ll have multiple rotational constants. The spectrum gets complicated quickly. In the limit of really big molecules, low-lying vibrations will have the same order energy as rotations. So there will still be more internal pathways for a state to decohere.

In the community that performs the experiments you linked to in OP, “polyatomic” usually means something like 3 or 4 atoms, so a lot of these concerns might be mitigated. I dunno, I’m not as familiar with the issues there. But you still could have problems with coupling to the trap states or pendular states, depending on how the ions are being contained. I’d have to read up on what exactly limits the coherence times of excited rotational states in trapped ion pairs in the first place.

 

[kelly0303]

I’m sorry, it sounded like you were asking why vibrational states in polyatomics are shorter-lived than in diatomics.

But even in the ground vibrational state probing rotational levels, if the molecule gets bigger, the rotational constant will decrease, and if the molecule is asymmetric, you’ll have multiple rotational constants. The spectrum gets complicated quickly. In the limit of really big molecules, low-lying vibrations will have the same order energy as rotations. So there will still be more internal pathways for a state to decohere.

In the community that performs the experiments you linked to in OP, “polyatomic” usually means something like 3 or 4 atoms, so a lot of these concerns might be mitigated. I dunno, I’m not as familiar with the issues there. But you still could have problems with coupling to the trap states or pendular states, depending on how the ions are being contained. I’d have to read up on what exactly limits the coherence times of excited rotational states in trapped ion pairs in the first place.

Thank you for this! My questions is indeed about molecules with a small number of atoms, not large molecules. So I am a bit confused about decoherence in this case (I don't really know much about the topic). The lowest few states have large lifetimes and hence very narrow linewidths. If I tune my laser to one of these transitions (assuming my laser is not super wide in frequency space), I will not interact with any other transition (assuming there are no accidental close to degeneracy levels). Also during the coherence time (e.g during the evolution after a $\pi/2$ pulse) the possibility of decaying to a lower level is very small due to the narrow linewidths. What exactly is causing an increase decoherence in this case, compared to atoms, or diatomic molecules?

 

[TeethWhitener]

What exactly is causing an increase decoherence in this case, compared to atoms, or diatomic molecules?

According to the Science article you linked to in OP, they explicitly mention blackbody radiation as being the main contributor to limits on the rotational state lifetimes of tens of milliseconds to seconds. Depending on the nature of the potential imposed by the ion trap, translational states within the trap could also become a problem.

Also from the SI of that paper:
"The number of accessible internal states grows quickly with increasing number of nuclei, hyperfine couplings, and spin-rotation couplings in a molecule. This poses a challenge for our heralded probabilistic state preparation...We speculate that, with further improvement, polyatomics including several nuclei could be studied with our techniques. If certain functional groups or symmetries exist in the molecule, the molecular level structure could be simpler and the technique could be applicable to molecules with even more nuclei. The true limits of the technique likely need to be found by future experiments."
This tracks with my thinking from my earlier post about the challenges of keeping larger molecules from quickly relaxing to an approximately thermal state.

 

[f95toli]

One thing worth considering is that unless you are using an ion trap of some sort (which I suspect would be hard for a large molecule) much(sometimes most) of the broadening is likely to come from other molecules. If what you are measuring is actually hosted in some other medium (e.g. a crystal) or in a liquid you can't just consider the states of the molecule, but also how it interacts with its neighbours.. In real experiments there will always be a compromise between the number of moleculess you can measure (more molecules -> more signal) and broadening due interactions.
If your molecule is inside a crystal you will also have phonons, other impurities etc.

I don't know much about using complex molecules for QIP, but in the areas I do know something about (rare-Earth's in crystals) these "practical" considerations are usually much more important than the properties of a single atom/ion. Sometimes it is as simple as the fact that we don't have good signal sources (microwave generators or lasers depending on frequency) for the really "good" transitions; if the frequency you need is a say a few hundred GHz the experiments will be very difficult.

You might want to have a look at papers on room temperature masers using organic mixed molecular crystals, it is not QIP but idea is of course to use the fact that linewidth can be very narrow.

 

[Twigg]

Whoops, looks like I'm a little late to the party here!

Unfortunately, as @kelly0303 hinted in the OP, the reason you don't currently see complicated molecules in quantum logic experiments has more to do with the boring details of state prep and readout than it does with the quantum logic technique itself. I would speculate (entirely based on gut feeling, don't take it too seriously) this will change in the future as novel techniques for molecular state prep are worked out by groups like Brian Odom's (and others I am probably forgetting).

The coherence time is less of an issue, because there's no law that says that these folks have to use ordinary rotational or vibrational degrees of freedom in the future. ACME III currently predicts that they'll get >10s coherence times in YbOH (we'll see how it actually turns out, due to real-world limits like BB radiation and field homogeneity) using the angular degree of freedom in their vibrational modes where the "O" atom revolves around the Yb-H axis. I'm sure someone smarter and more motivated than me can come up with a molecular ion with the same properties that could be used in a quantum logic experiment.

To me the big question is "why". Quantum logic is cool and all, but for metrology purposes recent history has shown (with one exception being the aluminum ion clock at NIST) that having more molecules is more better. This also applies to the OP's question about measuring isotope shifts (by the way, I couldn't open your link to the paper). Yes, I'm sure you could do it with molecules and quantum logic, you could also do it with brute force laser-induced fluorescence (LIF) spectroscopy, which doesn't require a specialized ion trap.