Direct measurement of the quantum wavefunction

Abstract

The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule. At present, the wavefunction is determined through tomographic methods, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems--for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

What dynamics can be expected for mixed states in two-slit experiments?

“…To conclude, we would like to highlight that experiments such as those reported in [1] or [2] precisely show that we are still far from a full exploitation of the possibilities offered by quantum mechanics. Actually, experiments targeting general quantum states have recently been proposed [35] and performed [36].…”

“…This landscape started changing in 2011, with experiments showing that it is possible to reconstruct the photon wave function from direct measurements [1] and to infer how photons travel (on average) in Young's experiment [2]. This apparent breach in the above principles is possible through the experimental implementation of the concept of weak measurement [3][4][5], which does not constitute a true violation of the quantum rules, but only looking at them with different eyes.…”

Understanding quantum measurement from the solution of dynamical models

“…It seems timely, not only for conceptual purposes but to help the development of realistic experiments, to work out further models, in particular for such quantum measurements in which the whole history of the process is used to gather information. In this context we should mention the so-called weak measurements [365] that (in a sense) minimize the back-action of the measurement device on the measured system, and -although they have certain counterintuitive features -can reveal the analogues of classical concepts in quantum mechanics; e.g., state determination with the minimal disturbance, classical causality [366,367,368,369,370,371], and even mapping out of the complete wave function [372] or of the average trajectories of single photons in a double-slit experiment [373].…”

What Is a Quantum-Mechanical “Weak Value” the Value of?

“…Not the least has the field opened up new tools for experimentalists to investigate aspects of phenomena that were thought impossible earlier. These include determining (even if only statistically) the trajectories in a double slit experiment without destroying the interference pattern [5], and directly measuring the wave function [6]. The use of the technique for amplification purposes has been spectacular [7][8][9].…”

“…Note that I do not here question the weak value as a measureable entity pertaining to the system under study, nor the many ingenious ways experimentalist have exploited the weak measurement + post-selection idea ( [5][6][7][8][9][11][12][13][14]; see also [3] for a brief review). What I do question is whether a weak value can be given an 'ordinary' meaning.…”