Quantum Jumps

Quantum Jumps

Detailed Description

Scientific context: 

Measurement: 

Understanding the behavior of quantum systems during measurement sits at the foundation of modern physics. Many quantum systems have an associated spectra or discrete set of values in which the system can be found- in the language of quantum mechanics these are referred to as eigenstates. For example, a valence electron bound to an ion can be described by a set of orbitals (the familiar s,p,d,f, etc. levels and their sub-levels) with each level corresponding to a particular energy value (often expressed in terms of the transition frequency with the relation E=hv). 

In an atomic system, transitions between these levels can be driven by the application of a laser with a frequency (a measure of the color of light) equal to the difference in energy between the two levels. Similarly, based on the principle of stimulated emission, the state of the electron can be measured by illuminating an ion with a laser tuned to a particular transition frequency. If the electron occupies an energy level with an accessible transition ‘on resonance’ (ie of the same frequency) with the applied laser light, the electron will be driven between the two states, emitting a photon of the same color. However, if the electron occupies a level without such a transition, no light will be emitted from the ion. Therefore, by observing the photon emission (or lack thereof), the state of the ion can be determined. This measurement scheme makes use of ‘state dependent fluorescence.’  

Time evolution: 

Quantum mechanics describes the way in which systems, such as the state of an electron in an ion, develop. The Schrodinger equation governs the coherent time evolution of such systems. In other words, the trajectory of quantum systems must be deterministic and described by a unitary time evolution operator. 

Unitary evolution of quantum systems implies the principle of superposition. This means that given a certain spectrum (or set of eigenstates) for a quantum system, like the electron energy levels described above, the state of the system can be prepared with a probability amplitude in multiple eigenstates.  

State collapse and quantum jumps: 

We have described how, upon measurement, quantum systems can only be found in a discrete set of states. On the other hand, during free evolution states can exist in superpositions of this basis and that the evolution of these systems is deterministic. The natural question then arises: ‘if an quantum state exists in a superposition, what happens during measurement?’ 

Debate on this topic, known as ‘the quantum measurement problem’ stretches back to the foundation of the field itself. The standard interpretation of the problem holds that measurement causes the state of the quantum system to ‘collapse’ stochastically and instantaneously to an eigenstate with a probability to be found in the resultant state related to the relative amplitude of each basis in the superposition directly before measurement. In other words, a probabilistic and immediate change of state replaces the ‘usual’ deterministic evolution of the quantum system. After collapse, the system should be ‘memoryless’ to its prior state and once again evolve freely according to the Schrodinger equation. 

Closely related to state collapse, the phenomena of quantum jumps refer to how transitions between states occur in a system under constant measurement. Because evolution must be continuous in time according to the Schrodinger equation, in order to drive a quantum system from one eigenstate to another (such as from 6S1/2 to 5D5/2 in 138Ba in fig 1), the system must go through a smooth evolution characterized by a superposition during the time required to complete the transition. What then will happen if such a transition is stimulated by the application of the appropriate laser field while the state of the system is being continuously measured (for example by detection of state dependent fluorescence along the S to P line using a 493 nm laser)? Measurement induces collapse therefore by continuously reading out the state of the system, the smooth evolution of the between eigenstates (like energy level for the electron) can be prevented, a dynamic known as the ‘Quantum Zeno paradox’. Still, these transitions have been shown to occur since as early as 1986. The approach to characterizing quantum transitions of systems under strong measurement, conventionally known as ‘quantum jumps’, has been ad hoc. The paradigm associated with these events holds that jumps are stochastic, non-unitary and instantaneous. 

As it stands, the dominant framework for understanding quantum state evolution has a bipartite, contradictory character: coherent evolution in the absence of measurement and non-unitary collapse or jumps when the state of the system can be determined. Efforts to resolve this discrepancy have largely related to applications of decoherence theory and allowing ‘system-observer’ entanglement. However, few studies have sought to tackle the problem of directly characterizing quantum jumps and state collapse head on due to the daunting technical challenges of achieving the high time resolution necessary to understand the dynamics of the quantum systems during the period directly preceding the jump. 

Recent findings in artificial atoms: 

Contrary to the traditional model of random, immediate jumps, in the last few years work on artificial super conducting atoms has demonstrated that quantum transitions in system under continuous measurement may actually be heralded, deterministic and even reversible. Researchers found that in a three-level artificial atom with a strong scattering line used for state detection and a weak transition used to stimulate jumps, the rate of photon collection along the detection path decreased in the period directly before a jump occurred. The existence of such a ‘latency period’ stands in contrast with the memoryless model of state collapse and supposedly instantaneous character of jumps. The latency period heralded the event, allowing the team to ‘catch and reverse’ the jump. If this work could be replicated in a highly isolated quantum system, such as a trapped ion, it would have profound implications for quantum fundamentals and also open new routes for state control. 

Our work: 

Experiments:

We work to characterize the dynamics of quantum jumps in trapped ions using specialized integrated optics and imaging systems which will allow us to generate record breaking time resolution pictures of what happens during these events. 

138Ba+ ions serve as our test bed with a strong, visible (493 nm) transition allowing doppler cooling (along with a 650 nm ‘repump’ line) and state readout. In our current system, we trap single ions at the focus of a parabolic mirror (fig 2) whose surfaces collects ~40% of the photons emitted by the ion. This collection efficiency, far superior to the 1-5% typical of lens based systems in most ion traps, allows a much higher time resolution of the quantum state. By application of a weak ‘shelving’ transition at 1762 nm, we will drive the electron to the 5D5/2 level and induce jumps. We aim to test the existence of jumps in a pristine atomic system.