Direct Measurement of the Quantum Wavefunction

Central to quantum theory, the wavefunction is the complex distribution used to completely describe a quantum system. 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 via the Born Rule. Presently, scientists determine the wavefunction through tomographic methods, which estimate the wavefunction that is 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 (i.e. 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 both to other degrees of freedom of the photon (e.g. polarization, frequency, etc.) and to other quantum systems (e.g. electron spin-z quantum state, SQUIDs, trapped ions, etc.). 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 scientists are able to characterize and initiate new avenues to understand fundamental quantum theory

Void-nanograting transition by ultrashort laser pulse irradiation in silica glass

The structural evolution from void modification to self-assembled nanogratings in fused silica is observed for moderate (NA > 0.4) focusing conditions. Void formation, appears before the geometrical focus after the initial few pulses and after subsequent irradiation, nanogratings gradually occur at the top of the induced structures. Nonlinear Schrödinger equation based simulations are conducted to simulate the laser fluence, intensity and electron density in the regions of modification. Comparing the experiment with simulations, the voids form due to cavitation in the regions where electron density exceeds 1020 cm-3 but is below critical. In this scenario, the energy absorption is insufficient to reach the critical electron density that was once assumed to occur in the regime of void formation and nanogratings, shedding light on the potential formation mechanism of nanogratings

Phenomena of ultrafast laser material modification with respect to spatio-temporal couplings of the laser pulse

The nano-structuring of transparent media with subpicosecond laser pulses has attracted significant interest due to its unique applications. In contrast to nanosecond pulses where the energy introduced to the lattice is absorbed, leading to melting/boiling of the material around the focal volume, femtosecond lasers can alter material properties of the glass at high pressures without excessive production of heat, modifying the structures with sub-micron resolution. Permanent modifications can then be induced without strong collateral damage. Although femtosecond pulses are beneficial for material processing, short pulse durations and broad spectral bandwidths require a novel approach to femtosecond pulse control.It is well known that laser induced modification depends on fluence, wavelength and polarization. Another dependence of material modification is the spatio-temporal properties of the ultrashort pulse. These spatio-temporal couplings give rise to intrinsic nonlinear optical phenomena, which are well known in experiment but otherwise lack a clear explanation. While the formation mechanisms with respect to the nano-structuring of transparent media is still under debate, a better understanding of the nonlinear optical phenomena that affects the formation would provide insight into the physics of ultrafast light-matter interaction.In this thesis, the origin and thorough investigation of spatio-temporal induced phenomena are reported. By controlling the spatio-temporal couplings separately, I demonstrate complete control of all of the dependencies with the use of prism compressors and grating compressors and discuss the intricacies behind the control of the spatio-temporal couplings with complete characterization of the pulse. By investigating two of the main phenomena associated with spatio-temporal couplings, which give rise to a directional dependence when writing in the bulk (“quill-writing effect”) and a photosensitive anisotropy (“blade effect”), a more thorough understanding of the light-matter interaction is demonstrated and reported.I demonstrate that spatio-temporal couplings are inherent for all ultrafast laser systems with chirped-pulse amplification and result in a strongly anisotropic light-matter interaction. I identify angular dispersion in the focus as the main cause for the anisotropic photosensitivity coming from the spatially chirped pulse, which shows to yield a 200% increase in modification strength. With tighter focusing (NA ≥ ~0.4), this non-paraxial effect leads to a more apparent manifestation of spatio-temporal couplings in photo-induced modification. I control the anisotropy and exploited it as a new degree of freedom in tailoring laser induced modification in transparent material. A non-paraxial field structure analysis near the focus is conducted, with an elliptical optical beam, to provide insight on the origin of the photosensitive anisotropy.After a complete identification of the spatio-temporal properties of the electric field, the quill-effect was confirmed to be due to pulse front tilt in the focus with a direct comparison with other major spatio-temporal couplings including wavefront rotation. I reveal that the non-reciprocity during femtosecond laser writing in transparent media induces either an isotropic damage-like structure or a self-assembled nanostructure depending on the movement direction of the beam - known as the “quill-writing effect.” I also identify the switching of the modification regime from the formation of isotropic damage-like to anisotropic grating-like structures observed when the translation of the beam is in the direction of the tilt and is qualitatively described in terms of the first-order phase transition in the irradiated volume of a transparent dielectric.The structural evolution from void modification to self-assembled nanogratings in fused silica for moderate (NA &gt; 0.4) focusing conditions is also discussed in this thesis. Void formation appears before the geometrical focus after the initial few pulses with nanogratings gradually occurring at the top of the induced structures after subsequent irradiation. Nonlinear Schrödinger equation-based simulations are conducted to simulate the laser fluence, intensity and electron concentration in the regions of modification. Comparing the experiment with simulations, the voids form due to cavitation in the regions where electron concentration exceeds 1020 cm-3 but remains below critical. In this scenario, the energy absorption is insufficient to reach the critical electron concentration that was once assumed to occur in the regime of void formation and nanogratings, shedding light on the potential formation mechanism of nanogratings.In-situ observations of harmonic generation during the ultrafast laser writing is presented to better understand the underlying physics that occur during the process of nanograting formation. Second and third harmonic generation is observed, with third harmonic distributed as two lobes following the polarization orientation of the electric field, identified as Cherenkov Third Harmonic. These harmonics are observed and correlated with the different regimes of material modification to understand whether they are part of the nanograting formation or corollary to give insight on the formation mechanisms of the self-assembled nanostructures.Finally, I discuss the work on the concept of an on-axial simultaneous spatio-temporal focusing with the use of a simple polarization dependent circular grating for the purpose of material modification using the expertise of the group on polarization gratings. The design and theoretical validation of the technique is reported in this thesis with the potential of further work in perfecting it for material modification and chirped-pulse amplification applications.</p

Unambiguous evidence of two plasmon decay during ultrafast laser writing in glass

The interaction of femtosecond laser pulses with transparent media has been a focus of research due to its unique properties. It has been established that above a certain threshold, self-assembled nanogratings in silica glass can be induced [1]. Although the mechanism that triggers the nanostructure is still unclear, a theory has been introduced involving the mechanism of nanogratings formation based on two plasmon parametric decay [2]. A signature of two-plasmon decay is the generation of the 3/2 harmonic. Previously, in transparent media, only a weak 3ω/2 emission was observed at high energy thresholds [3]. Thus it remains unclear if two plasmon decay can be associated with self-assembled nanogratings formation. Here we present a thorough survey of 2nd, 3rd and 3/2 harmonic generations in fused silica for varying laser fluences within multiple regimes of optical laser writing and self-assembled nanostructures. We demonstrate that 3ω/2 can be observed at the energies close to the threshold of permanent material modification

Direct Writing with Tilted-Front Femtosecond Pulses

Dataset supporting the article Direct Writing with Tilted-Front Femtosecond Pulses by Aabid Patel, Yuri Svirko, Charles Durfee, and Peter G. Kazansky in Scientific Reports</span

Dataset for Non-Paraxial Polarization Spatio-Temporal Coupling in Ultrafast Laser Material Processing

Dataset supporting the article Non-Paraxial Polarization Spatio-Temporal Coupling in Ultrafast Laser Material Processing by Aabid Patel, Vladmir T. Tikhonchuk, Jingyu Zhang, and Peter G. Kazansky in Laser and Photonics Review </span

3/2 harmonic generation - the clue to the mechanism of ultrafast laser nanostructuring

The correlation between (3/2)omega harmonic generation and self-assembling nanostructuring during ultrafast laser writing in glass has been observed. Interference between light and two-plasmon decay is proposed

Non-paraxial polarization spatio-temporal coupling in ultrafast laser material processing

Two hundred years after Malus' discovery of optical anisotropy, the study of polarization driven optical effects is as active as ever, generating interest in new phenomena and potential applications. However, in ultrafast optics, the influence of polarization is frequently overlooked being considered as either detrimental or negligible. Here we demonstrate that spatio-temporal couplings, which are inherent for ultrafast laser systems with chirped-pulse amplification, accumulate in multi pulse irradiation and lead to a strongly anisotropic light-matter interaction. Our results identify angular dispersion in the focus as the origin for the polarization dependence in modification, yielding an increase in modification strength. With tight focusing (NA ≥ ~0.4), this non-paraxial effect leads to a manifestation of spatio-temporal couplings in photo-induced modification. We devise a practical way to control the polarization dependence and exploit it as a new degree of freedom in tailoring laser-induced modification in transparent material. A near-focus, non-paraxial field structure analysis of an optical beam provides insight on the origin of the polarization dependent modification. However, single pulse non-paraxial corrected calculations are not sufficient to explain the phenomena confirming the experimental observations and exemplifying the need for multi-pulse analysis

Direct writing with tilted-front femtosecond pulses

Shaping light fields in both space and time provides new degrees of freedom to manipulate light-matter interaction on the ultrafast timescale. Through this exploitation of the light field, a greater appreciation of spatio-temporal couplings in focusing has been gained, shedding light on previously unexplored parameters of the femtosecond light pulse, including pulse front tilt and wavefront rotation. Here, we directly investigate the effect of major spatio-temporal couplings on light-matter interaction and reveal unambiguously that in transparent media, pulse front tilt gives rise to the directional asymmetry of the ultrafast laser writing. We demonstrate that the laser pulse with a tilted intensity front deposits energy more efficiently when writing along the tilt than when writing against, producing either an isotropic damage-like or a birefringent nanograting structure. The directional asymmetry in the ultrafast laser writing is qualitatively described in terms of the interaction of a void trapped within the focal volume by the gradient force from the tilted intensity front and the thermocapillary force caused by the gradient of temperature. The observed instantaneous transition from the damage-like to nanograting modification after a finite writing length in a transparent dielectric is phenomenologically described in terms of the first-order phase transition