We present surprising experimental evidence regarding the past of photons passing through an interferometer. The information about the positions through which the photons pass in the interferometer is retrieved from modulations of the detected signal at the vibration frequencies of mirrors the photons bounce off. From the analysis we conclude that the past of the photons is not represented by continuous trajectories, although a "common sense" analysis adopted in various welcher weg measurements, delayed-choice which-path experiments, and counterfactual communication demonstrations yields a single trajectory. The experimental results have a simple explanation in the framework of the two-state vector formalism of quantum theory.

We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to $77$ K suppresses longitudinal spin relaxation $T_1$ effects and DD microwave pulses are used to increase the transverse coherence time $T_2$ from $\sim 0.7$ ms up to $\sim 30$ ms. We extend previous work of single-axis (CPMG) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the optimal control scheme for preserving an arbitrary spin state is a recursive protocol, the concatenated version of the XY8 pulse sequence. The improved spin coherence might have an immediate impact on improvements of the sensitivities of AC magnetometry. Moreover, the protocol can be used on denser diamond samples to increase coherence times up to NV-NV interaction time scales, a major step towards the creation of quantum collective NV spin states

The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness against such fluctuations in a dense ensemble of nitrogenvacancy centers in diamond. Considering realistic experimental errors in the system, we identify the optimal modulation strength, and demonstrate an improvement of an order of magnitude in the spinpreservation of arbitrary states over conventional single continuous driving. The phase-modulated driving exhibits comparable results to previously examined amplitude-modulated techniques, and is expected to outperform them in experimental systems having higher phase accuracy. The proposed technique could open new avenues for quantum information processing and many body physics, in systems dominated by high-frequency spin-bath noise, for which pulsed dynamical decoupling is less effective. PACS numbers: 76.30.MiOne of the main challenges in quantum information processing, quantum computing and quantum sensing is the preservation of arbitrary spin states. For example, the sensitivity of nitrogen-vacancy (NV) ensemble-based AC magneteometry scales as a square-root of the coherence time [1][2][3][4][5][6][7][8]. Moreover, long ensemble spin coherence times could open new avenues for studying many body dynamics of interacting spins [9][10][11]. The commonly used technique for improving coherence times and preserving arbitrary states is dynamical decoupling (DD) sequences [12][13][14][15][16][17][18]. Although pulsed DD is very efficient for a variety of physical systems, continuous driving-based decoupling (i.e. spin-lock) has an advantage when the power spectrum of the noise bath contains a significant contribution from high-frequency terms, such that relevant correlation times are shorter than the duty cycle achievable by pulsed techniques [15,16]. However, in these continuous schemes, amplitude fluctuations of the driving source itself limit the achieved coherence times, raising the need for a fault tolerant driving [16,[18][19][20][21][22][23].One common approach for overcoming fluctuations in the driving amplitude is to flip the phase of the continuous driving every time increment τ (i.e., to apply a "rotary echo", [24]). However, in the basis of the dressed states, these techniques are equivalent to pulsed DD, having the same disadvantages, such as additional imperfections due to the application of non-ideal pulses, and the disability of mitigating amplitude fluctuations that are faster than the flipping rate 1/τ . Another approach for overcoming these fluctuations is to apply an additional continuous driving in the perpendicular axis [ Fig. 1(a)]. In order to avoid the use of an extra microwave (MW) source, the same effective Hamiltonian can be generated by a time-dependent modulation of the amplitude or phase of the original driving. Recently, such time-dependent amplitude modulation was experimentally demonstrated in a system o...

The modification of the effect of interactions of a particle as a function of its preselected and postselected states is analyzed theoretically and experimentally. The universality property of this modification in the case of local interactions of a spatially preselected and postselected particle has been found. It allowed us to define an operational approach for the characterization of the presence of a quantum particle in a particular place: the way it modifies the effect of local interactions. The experiment demonstrating this universality property provides an efficient interferometric alignment method, in which the position of the beam on a single detector throughout one phase scan yields all misalignment parameters.

The studies of many-body dynamics of interacting spin ensembles, as well as quantum sensing in solid state systems, are often limited by the need for high spin concentrations, along with efficient decoupling of the spin ensemble from its environment. In particular, for an ensemble of nitrogenvacancy (NV) centers in diamond, high conversion efficiencies between nitrogen (P1) defects and NV centers are essential, while maintaining long coherence times of an NV ensemble. In this work, we study the effect of electron irradiation on the conversion efficiency and the coherence time of various types of diamond samples with different initial nitrogen concentrations. The samples were irradiated using a 200 keV transmission electron microscope (TEM). Our study reveals that the efficiency of NV creation strongly depends on the initial conversion efficiency as well as on the initial nitrogen concentration. The irradiation of the examined samples exhibits an order of magnitude improvement in the NV concentration (up to ∼ 10 11 NV/cm 2 ), without degradation in their coherence times of ∼ 180 µs. We address the potential of this technique toward the study of many-body physics of NV ensembles and the creation of non-classical spin states for quantum sensing. The study of quantum many-body spin physics in realistic solid-state platforms has been a long-standing goal in quantum and condensed-matter physics. In addition to the fundamental understanding of spin dynamics, such research could pave the way toward the demonstration of non-classical spin states, which will be useful for a variety of applications in quantum information and quantum sensing. One of the leading candidates for such studies is the negatively charged nitrogen-vacancy (NV) center in diamond, having unique spin and optical properties, which make it useful for various sensing applications [1][2][3][4][5][6][7][8][9], as well as a resource for quantum information processing and quantum simulation [10][11][12].The current state-of-the-art is limited by the requirement of obtaining high spin concentrations while maintaining long coherence times. The sensitivity of magnetic sensing grows as the square-root of the number of spins [1,3], thus enhanced NV concentrations could improve magnetometric sensitivities. Furthermore, enhanced NV concentrations could lead to strong NV-NV couplings, which together with long coherence times, achieved using a proper dynamical decoupling protocol [13], could pave the way toward the study of many-body dynamics in the NV-NV interaction-dominated regime [10][11][12]. However, nitrogen defects not associated with vacancies (P1 centers) create randomly fluctuating magnetic fields that cause decoherence of the quantum state of the NV ensemble [14,15]. As a result, in most cases it would be beneficial to increase the concentration of NV centers while keeping the nitrogen concentration constant, i.e. improve the N to NV conversion efficiency.A common technique for improving the conversion efficiency is the irradiation of the sample with elec...

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Magnetization in rock samples is crucial for paleomagnetometry research, as it harbors valuable geological information on long term processes, such as tectonic movements and the formation of oceans and continents. Nevertheless, current techniques are limited in their ability to measure high spatial resolution and high-sensitivity quantitative vectorial magnetic signatures from individual minerals and micrometer scale samples. As a result, our understanding of bulk rock magnetization is limited, specifically for the case of multi-domain minerals. In this work we use a newly developed nitrogen-vacancy magnetic microscope, capable of quantitative vectorial magnetic imaging with optical resolution. We demonstrate direct imaging of the vectorial magnetic field of a single, multi-domain dendritic magnetite, as well as the measurement and calculation of the weak magnetic moments of an individual grain on the micron scale. These results pave the way for future applications in paleomagnetometry, and for the fundamental understanding of magnetization in multi-domain samples.When igneous rocks in Earth's crust are formed by cooling of hot magma they acquire thermoremanent magnetization (TRM) parallel and proportional to the ambient field at the time of cooling. TRM can remain stable for millions of years preserving valuable geological magnetic information on complex long term processes, such as plate tectonic movements and formations of oceans and continents [1]. Despite its importance, little is known on the details of how thermoremanent magnetic information is acquired and retained in rocks [2]. Paleomagnetism, the science of studying natural magnetic information, heavily relies on Néel theory [3] of single-domain (SD) minerals. Yet, the dimensions of rock-forming minerals typically exceed the sub-micrometric threshold size for SD. As such, TRM is mostly held by multi-domain (MD) particles rather than by SD. In the absence of a general analytical formulation for TRM in MD, there is a growing need for direct observations of natural MD magnetization. Particularly, vectorial imaging of magnetic fields generated by MD particles with sub-micron spatial resolution and micrometer scale sample-detector distance, along with high sensitivity (µT / √ Hz), is critical for understanding the mechanism controlling the geometry and size of MD arrangements, the total moment exerted by individual natural crystals, and the stability of MD magnetic information over geological times.There are a number of magnetic imaging techniques that have been used in paleomagnetic research in a complementary fashion: Kerr effect [4] , Magnetic Force Microscopy (MFM) [5], electron holography [6], and SQUID microscopy [7]. Recently, a newly developed method based on nitrogen-vacancy (NV) magnetic microscopy [8][9][10], has been demonstrated by [11,12] in the context of paleomagnetometry. NV magnetic microscopy enables direct measurements of the three components of the magnetic field vector at a constant height above the sample in a room temperature environ...

In this work, we simulate the dynamics of varying density quasi-2D spin-ensembles in solid state systems, focusing on the Nitrogen-Vacancy (NV) centers in diamond. We consider the effects of various control sequences on the averaged dynamics of large ensembles of spins, under a realistic "spin-bath" environment. We reveal that spin-locking is efficient for decoupling spins initialized along the driving axis, both from coherent dipolar interactions, and from the external spin-bath environment, when the driving is two orders of magnitude stronger than the relevant coupling energies. Since the application of standard pulsed dynamical decoupling (DD) sequences leads to strong decoupling from the environment, while other specialized pulse sequences can decouple coherent dipolar interactions, such sequences can be used to identify the dominant interaction type. Moreover, a proper combination of pulsed decoupling sequences could lead to the suppression of both interaction types, allowing additional spin manipulations. Finally, we consider the effect of finitewidth pulses on these control protocols, and identify improved decoupling efficiency with increased pulse duration, resulting from the interplay of dephasing and coherent dynamics.