Mayukh Lahiri's research while affiliated with Oklahoma State University - Stillwater and other places

We present a quantum interference phenomenon in which four-photon quantum states generated by two independent sources are used to create a two-photon interference pattern without detecting two of the photons. Contrary to the common perception, the interference pattern can be made fully independent of phases acquired by the photons detected to construct it. However, it still contains information about spatially dependent phases acquired by the two undetected photons. This phenomenon can also be observed with fermionic particles. We show that the phenomenon can be applied to develop an interferometric, quantum phase imaging technique that is immune to uncontrollable phase fluctuations in the interferometer and allows image acquisition without detecting the photons illuminating the object.

The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key ingredients are (i) employing an additional qubit, (ii) aligning the undetected qubit with a known reference state by using path identity, and (iii) measuring the additional qubit to reconstruct the undetected qubit state. We establish theoretically and demonstrate experimentally the method with photonic polarization states. The principle underlying our method could also be applied to quantum entities other than photons.

Conventional methods of measuring entanglement in a two-qubit photonic mixed state require detection of both qubits. We generalize a recently introduced method which does not require detection of both qubits, by extending it to cover a wider class of entangled states. Specifically, we present a detailed theory that shows how to measure entanglement in a family of two-qubit mixed states, obtained by generalizing Werner states, without detecting one of the qubits. Our method is interferometric and does not require any coincidence measurement or postselection. We also perform a quantitative analysis of anticipated experimental imperfections. We show that the method is resistant to a decrease in the interference visibility resulting from such imperfections.

Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.

Conventional methods of measuring entanglement in a two-qubit photonic mixed state require the detection of both qubits. We generalize a recently introduced method which does not require the detection of both qubits, by extending it to cover a wider class of entangled states. Specifically, we present a detailed theory that shows how to measure entanglement in a family of two-qubit mixed states - obtained by generalizing Werner states - without detecting one of the qubits. Our method is interferometric and does not require any coincidence measurement or postselection. We also perform a quantitative analysis of anticipated experimental imperfections to show that the method is experimentally implementable and resistant to experimental losses.

Measuring entanglement is an essential step in a wide range of applied and foundational quantum experiments. When a two-particle quantum state is not pure, standard methods to measure the entanglement require detection of both particles. We realize a conceptually new method for verifying and measuring entanglement in a class of two-part (bipartite) mixed states. Contrary to the approaches known to date, in our experiment we verify and measure entanglement in mixed quantum bipartite states by detecting only one subsystem, the other remains undetected. Only one copy of the mixed or pure state is used but that state is in a superposition of having been created in two identical sources. We show that information shared in entangled systems can be accessed through single-particle interference patterns. Our experiment enables entanglement characterization even when one of the subsystems cannot be detected, for example, when suitable detectors are not available.

Interferometric methods, renowned for their reliability and precision, play a vital role in phase imaging. Interferometry typically requires high coherence and stability between the measured and the reference beam. The presence of rapid phase fluctuations averages out the interferogram, erasing the spatial phase information. This difficulty can be circumvented by shortening the measurement time. However, shortening the measurement time results in smaller photon counting rates precluding its applicability to low-intensity phase imaging. We introduce and experimentally demonstrate a phase imaging technique that is immune to position-independent, time-dependent phase fluctuation. We accomplish this by measuring intensity correlation instead of intensity. Our method enables using long measurement times and is therefore advantageous when the photon flux is very low. We use a Fisher information-based approach to show that the precision of phase reconstruction achieved using our method is in fact the best achievable precision in the scenario when two photons are detected per phase stability time.

We present a novel, quantum interferometric method of measuring entanglement of a family of two-photon mixed states that are obtained by generalizing Werner states. The method does not require detecting one of the photons.

The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key ingredients are: (i) employing an additional qubit, (ii) aligning the undetected qubit with a known reference state by using path identity, and (iii) measuring the additional qubit to reconstruct the undetected qubit state. We theoretically establish and experimentally demonstrate the method with photonic polarization states. The principle underlying our method could also be applied to quantum entities other than photons.

We present a tutorial on the phenomenon of induced coherence without induced emission, and specifically its application to imaging and metrology. It is based on a striking effect where two nonlinear crystals, by sharing a coherent pump and one or two output beams, can induce coherence between the other two output beams. This can be thought of as a type of quantum-erasure effect, where the “welcher-weg” (which-way), or in this case, “which-source,” information is erased when the shared beams are aligned. With the correct geometry, this effect can allow an object to be imaged using only photons that have never interacted with the object—in other words, the image is formed using undetected photons. Interest in this and related setups has been accelerating in recent years due to a number of desirable properties, mostly centered around the fact that the fields for detection and imaging (since separate) may have different optical properties, entailing significant advantages for various applications. The purpose of this tutorial is to introduce researchers to this area of research, to provide practical tools for setting up experiments as well as understanding the underlying theory, and also to provide a comprehensive overview of the sub-field as a whole.