Controlling quantum mechanical entanglement in attosecond pump-probe experiments
Quantum mechanics is famous for the way its predictions challenge intuitive human thought developed through the way we experience the everyday world around us. Among other things, quantum objects can display both particle and wave character, can interfere, and can occur as quantum superimpositions.
Perhaps the greatest challenge of all is that quantum mechanics does not adhere to our intuitive notion of local realism, that is, the notion that the results of measurements on objects reflect the properties inherent in those objects. objects. Quantum mechanical entanglement represents a break from local realism and introduces the existence of non-locality, which implies that the results of measurements on an object A (“Alice”) can be influenced by measurements on an object B (“Bob”), without there being any interaction between objects A and B.
Entanglement occurs naturally when a quantum system is split into two subsystems. Common situations are spontaneous parametric downconversion, where an incoming pump photon is split into a pair of signal and inactive photons, and photoionization, where the absorption of light splits a neutral atom or molecule into an ion and a photoelectron. Then the total system wave function can be written as the sum of one or more product wave functions describing the individual parts.
If the wave function can be written as a single product, then measurements made on part A (“Alice”) do not affect measurements made on part B (“Bob”). However, if the wave function of the composite system can only be written as a sum of such products, then the system is entangled and the remarkable result emerges that the measurements on “Bob” (with different possible results depending on the quantum probability- mechanics of each of these results) will determine the result of subsequent measurements on “Alice”, even if “Alice” and “Bob” do not interact.
Based on the above, we can expect quantum entanglement to be a common feature in attosecond science (1 as = 10-18 s), the new branch of laser physics that emerged at the beginning of this century, where the time-dependent dynamics of electrons are studied over its natural, sub-femtosecond (1 fs = 10-15 s) time scale.
Generating attosecond laser pulses via high harmonic generation necessarily produces laser pulses with photon energies that exceed the binding energy of every imaginable atom, molecule, or material, and therefore photoionization is a common aspect attosecond experiments. Yet, until now, the possible role of entanglement in attosecond experiments has not received significant attention.
Attosecond experiments are typically performed as a pump-probe experiment, where a first laser (the “pump”) initiates a dynamic of interest in the system under study and, after a variable delay, a second laser (the ” probe”) interrogates the evolving system, producing a measurable observable as a function of the pump-probe delay. In this way, pump-probe experiments provide a movie of the evolving dynamics, which can be viewed repeatedly and slowly (frame by frame, if necessary) until the underlying processes are understood.
In terms of quantum mechanics, pump-probe experiments rely on coherence, i.e. the existence of well-defined phase relationships between the different parts of the system that forms after interaction with the pump laser pulse. . As we have shown in recent theories and experimental work, the degree of coherence is greatly reduced in quantum systems that display entanglement.
In experiments and in calculations, molecules of neutral hydrogen (H2) were ionized using an attosecond pulse, producing an H2+ ion in the lowest bound electronic state available. In this state, a vibrational wave packet has formed, that is, a coherent superposition of vibrational states, describing the vibration of the molecule between an inner and outer turning point.
The vibration was detected using a near-infrared probe laser, which dissociated the molecule, producing an easily detectable H+ ion and a neutral H atom. Since the probability of this dissociation process strongly depends on the internuclear distance between the two protons, the experiment could observe the vibration of the molecule by monitoring the fraction of molecules close to the outer inflection point of the vibration as a function of the pump-probe delay. Consistent with previous experimental results, the H2+ the vibrations could be easily measured, demonstrating the consistency between the different H2+ vibrational states.
This situation changed dramatically when the attosecond ionization pulse was replaced by a pair of phase-locked attosecond ionization pulses, with a controlled relative delay. For certain values of the delay, the H2+ the vibrations could be observed as before, whereas for other values the vibrations became practically unobservable. An analysis of time delays for which vibrational coherence was (un)observable, revealed that the degree of vibrational coherence in the H2+ cation occurred in competition with the degree of entanglement between the H2+ ion and the photoelectron produced in the ionization process.
In other words, the experiment provided direct evidence that in attosecond pump-probe experiments involving ionization, the entanglement between ion and photoelectron which are produced by ionization by the pump laser pulse, limits the coherence that can be observed when the probe laser interacts with the ion or photoelectron.
As such, the experiment provides an important warning to the attosecond community, demonstrating that the outcome of pump-probe experiments is governed by properties of the wave function of the full quantum system, even when the experiment cannot target than observing the dynamics in one of the subsystems.
The experiment also points to an interesting opportunity in, for example, studies aimed at the observation of attosecond to femtosecond charge migration, where the specific electronic coherences underlying the charge migration process can be revealed. Finally, these experiments draw attention to the emerging link between ultrafast laser spectroscopy and the field of quantum information, where the application of attosecond scientific research tools may create hitherto unsuspected opportunities.