List of Publications:

(Principal Author)

1.        Akbar, A., Khalid, M. W., and Anwar, M. S. ( 2017 ). ``Low temperature Voigt effect in the terbium gallium garnet crystal".  Optics Express,  25 ( 24 ),  30550 -- 30559 .

2.        Akbar, A., Saleem, M., Atiq, S., and Anwar, M. S. ( 2018 ). ``Magnetic Dynamics and All-Optical Switching in  5  nm Dy–Fe Nanostructures",  IEEE Transactions on Magnetics,  54 ( 7 ),  1 -- 6 .

(Collaborating Author)

3.       Mahmood, N., Kim, I., Mehmood, M.Q., Jeong, H., Akbar, A., Lee, D., Saleem, M., Zubair, M., Anwar, M.S., Tahir, F.A. and Rho, J., ( 2018 ). ``Polarisation insensitive multifunctional metasurfaces based on all-dielectric nanowaveguides", Nanoscale,  10 ( 38 ), pp. 18323 -- 18330 .

4.       Fatima, T., Akbar, A., Anwar, M.S. and Tahir, M.N., 2019. ``Six new dinuclear Schiff base complexes of Cu (II)/Ln (III) system: Synthesis, characterization and magnetic studies",  Journal of Molecular Structure,  1184 , pp. 462 -- 467 .

5.       Mahmood, N., Jeong, H., Kim, I., Mehmood, M.Q., Zubair, M., Akbar, A., Saleem, M., Anwar, M.S., Tahir, F.A. and Rho, J., 2019. ``Twisted non-diffracting beams through all dielectric meta-axicons",  Nanoscale,  11 ( 43 ), pp. 20571 -- 20578 .

               6. Abbas, S.K., Akbar, A., Atiq, S., Saleem, M., Iftikhar, M., Rafiq, H.M., Naseem, S. and Anwar, M.S., 2019. ``Optimization of DyFe nanostructures using E-beam lithography for magneto-optical applications", Journal of Magnetism and Magnetic Materials,  469 , pp. 196 -- 202 .

دوجہتی کوانٹم مادوں میں مقناطیسی نوریات کے مظاہر

خلاصہ

اس مقالے کا بنیادی مقصد دوجہتی کوانٹم مادوں میں مقناطیسی نوریات کے مظاہر کی دریافت ہے۔ کسی مقناطیسی میدان میں مادہ اور روشنی کے تعامل کے نتیجے میں روشنی کے تقطیبی خواص کے مطالعے کو مقناطیسی نوریات میں شمار کیا جاتا ہے۔ اِن خصوصیات کا استعمال بصری مواصلاتی ٹیکنالوجی، مقناطیسی میدانوں کی پیمائش اور لیزر کے شعبوں میں ہوتا ہے۔ اس مقالے میں کچھ ایسے ہی مشاہدات پیش کیے گئے ہیں۔ ہم نے اس مقالے کو آسانی کی خاطر تین حصوں میں تقسیم کیا ہے۔

پہلے حصے میں ہم نے دو جہتی کوانٹم مادوں کے خواص کو سمجھنے کے لیے طبیعیات کے بنیادی تصورات کا جائزہ لیا ہے جن میں مقامیاتی بینڈ نظریہ1، مقامیاتی متغیرات2، وقتی استرداد کا توازن3 اور مقامیاتی حاجز4 کا تعارف شامل ہے۔ ہم نے گریفین اور سلیسین (بالترتیب کاربن اور سیلیکان کے دو جہتی بہروپ) کی برقیاتی خصوصیات کی ڈراک طبیعیات سے جانچ پڑتال کی اور ان سے منسلک توانائی کے انتشار کے کلیے بھی اخذ کیے جو جدید تحقیق میں بنیادی نوعیت کے حامل اور کوانٹم مادوں کے جامع اور تفصیلی جائزے کے لیے ناگزیر ہیں۔

دوسرے حصے میں ہم نے مقناطیسی نوریات کے نتیجے میں ہونے والی روشنی کی گردش کا مطالعہ کیا گیا جو بالترتیب روشنی کی انعکاس 5 اور ترسیلی 6 جیومیٹری سے منسلک ہیں۔ یہ گھومنے کا عمل دو طرح سے بیان کیا جاتا ہے۔ جب مادے پر روشنی گر کر واپس پلٹ جائے تو اس کو گردشِ کر7، جبکہ یہی عمل اگر اس طرح واقع ہو کہ روشنی مادے میں سے آر پار گزر جائے، تو اس کو گردشِ فاراڈے8 کہتے ہیں۔ ان مظاہر کو نیم کلاسیکی اصولوں اور قواعد کے مطابق سیلیسین اور اس کے مماثل مادوں (جرمانین اور ٹنیین) میں پرکھا گیا ہے ۔ ان مادوں کی نمایاں اور ممتازخوبیوں میں سر فہرست خوبی، سپن مدارتی تعامل9 کا موجود ہونا ہے جو مادہ کے خواص میں تبدیلی کے لیے ایک نئی جہت مہیا کرتی ہے ۔ ہم نے دریافت کیا ہے کہ ۵ ٹیسلا کے مقناطیسی میدان میں حیران کن حد تک بڑی گردشِ کر دیکھی جاتی ہے ۔ جبکہ اس طرح کے تجربات میں عمومی طور پر دوسرے مادوں میں گردش محض ۵ یا ۶ ڈگری تک ہوتی ہے۔ مزید یہ کہ مقناطیسی اور برقی محرکات کی موجودگی میں مقامیاتی حاجز میں ان رجحانات کا تجزیہ،معمولی اور غیر معمولی مقامیاتی صورتوں کے درمیان کوانٹم مرحلہ وار منتقلی کی راہ ہموار کرتا نٖظر آتا ہے۔ امید ہے کہ یہ کھوج طبیعیات کے معروف مضمون کوانٹم تھیوری کے گوناگوں کرشمات کو انسانی عقل و فہم کے مزیدقریب لانے میں مدد دے گی۔

اس مقالے کا تیسرا اور آخری حصہ گوس ہانشین10 اور فوٹانک سپن ہال 11کے نتیجے میں وجود پذیرطولی اور زاویائی تبدیلیوں کے لیے مختص کیا گیا ہے۔ دو جہتی ٹوپولوجیکل مادے پر روشنی گرنے سے نت نئے بدلتے زاویوں کی تحقیق سے بائیوسینسرز کے ارتقا میں جدت لائی جا سکے گی اور مقناطیسی قوت ناپنے والے آلات کو بھی مزید بہتر بنایا جا سکے گا۔ طولی تبدیلی12 سے مراد روشنی کی مسلسل لہروں کا اپنے نقطہ ٹکراؤ کی بجائے طولی فاصلہ طے کر کے منعکس ہونا جبکہ زاویاتی تبدیلی 13روشنی کا اپنے سطح وقوع سے باہر نکل جانا ہے۔ ہم نے ان رجحانات کا مطالعہ دو جہتی کوانٹم مادوں میں برقی اور مقناطیسی محرکات کی موجودگی میں کیاہے۔ خالص نظریاتی بنیاد پر وضع کیے گیے کلیوں کے تجز یےسے یہ بات سامنے لائی گئی ہےکہ ان رجحانات(مثبت یا صنفی) کی مقدارکوانٹم مادوں میں بڑھ جاتی ہے۔مزید یہ کہ ان کی مقدارکو زاویہ انعطاف14 کے رد و بدل (بروسٹر زاویہ کے قرب میں) سے قابو کیا جا سکتا ہے۔

1. Topological band theory; 2. Topological variables; 3. Time-reversal symmetry; 4. Topological insulators; 5. Reflected; 6. Transmitted; 7. Kerr effect; 8. Faraday rotation; 9. Spin-orbit interaction; 10. Goos–Hänchen shift; 11. Photonic spin Hall effect; 12. Longitudinal displacement; 13. Angular displacement; 14. Brewster angle

Abstract

Recent developments in quantum materials with emergent properties are opening alternative avenues for materials engineering on demand. In quantum materials, collective electrons demonstrate various macroscopic behavior, typically in the presence of external stimuli i.e., electromagnetic fields. The main theme of this thesis is to explore magneto-optic phenomena in two-dimensional quantum materials which show promise for optical communication technology, remote sensing of magnetic fields, and other laser applications.

The central body of this work explores magneto-optic effects and mechanical beam shifts in these 2D quantum materials. For the sake of clarity, we have divided the thesis into three parts. First, we focus on some basic concepts of condensed matter physics which are important for understanding this thesis. The theoretical pursuit involves topological band theory, topological invariants, the description of the classical and quantum Hall effects, time-reversal symmetry, and introduction to 2D and 3D topological insulators. We discuss the electronic properties of graphene and silicene by studying their low-energy Dirac physics using tight-binding approximations. We also derive the energy dispersion in the presence of a magnetic field. To drive topological quantum phase transition between trivial and non-trivial states, we utilize the electric and magnetic fields as a control knob. Furthermore, we focus on the transport properties providing the theoretical framework.

Second, we focus on the magneto-optic responses of 2D silicene and hybridized topological insulators. The behavior of these quantum materials under the influence of external fields, for example, electric and magnetic fields, is dictated in a highly non-trivial manner including the possibility of topological phase transitions. The presence of strong spin-orbit interaction in silicene and its analogues, germanene and tinene, also leads to the opening of a gap in the energy spectrum and spin-splitting of the bands in each valley. We use a semiclassical treatment to describe the Faraday rotation (FR) and Magneto-optic Kerr effect (MOKE) which can be modulated both electrically and magnetically. We derive analytical expressions for the valley and spin-polarized FR and MOKE for arbitrary polarization of incident light in the terahertz regime. All in all, very large FR and MOKE can be achieved.

We also discuss the magneto-optic response of topological insulator (TI) thin films exposed to quantizing, external magnetic fields. We theoretically investigate quantum phase transitions from topologically non-trivial to trivial states and vice versa in three-dimensional hybridized topological insulators ultra-thin films. The interplay between the hybridization of the top and bottom surface states (SSs) and Zeeman energy also gives rise to topological and normal insulating phases. Therefore, by tuning the Zeeman energy, we can drive the phase transition between these two phases. Furthermore, we impinge a Gaussian beam on the surface of the 3D TI to study FR MOKE in the presence of an external magnetic field, while explicitly taking into account the hybridization between the top and bottom Dirac SSs of the TI film.

The third part of the thesis is devoted to Goos-Hanchen and photonic spin Hall shifts for light beams impinging on the surface of 2D quantum material-substrate systems in the terahertz regime. We show that giant positive and negative quantized spatial and angular beam shifts can be obtained by tuning the angle of incidence in the vicinity of the Brewster angle. We demonstrate that the in-plane and transverse spatial spin-dependent shifts are quantized due to the Landau level (LL) quantization of the magneto-optic conductivities.

List of publications during Ph.D.

[1] Muzamil Shah and Muhammad Sabieh Anwar, ``Magneto-optical effects in the Landau level manifold of 2D lattices with spin-orbit interaction," Opt. Express 27, 23217-23233 (2019).

[2] Muzamil Shah and Muhammad Sabieh Anwar, ``Magneto-optic modulation of lateral and angular shifts in spin-orbit coupled members of the graphene family," OSA Continuum, 3, 878 (2020).

[3] Muzamil Shah and Muhammad Sabieh Anwar, ``Quantized and topological photonic spin Hall effects in the graphene family in the presence of magnetic fields," OSA Optical Sensors and Sensing Congress (2020).

[4] Muzamil Shah, Ali Akbar, Muhammad Sajid and Muhammad Sabieh Anwar, `` Transitional Faraday and Kerr effect in hybridized topological insulator thin films” Opt. Mat. Express 11, 525-538 (2021).

[5] Muzamil Shah and Muhammad Sabieh Anwar, ``Valley and spin polarized quantized spin dependent photonic shifts in topological silicene," Physics Letters A, 127342 (2021).

[6] Muzamil Shah, Muhammad Sajid and Muhammad Sabieh Anwar, ``Quantized Goos-Hanchen shifts on the surface of hybridized topological insulator thin films," Physica E: Low-dimensional Systems and Nanostructures, p. 114819 (2021).

[7] Muzamil Shah, Mudasir Shah and Ali Akbar, ``Magnetically tunable Goos-Hanchen shifts in topological quantum materials," CLEO OSA (2021).

[8] Muzamil Shah, Muhammad Sajid and Mudasir Shah, ``Magnetic field and Fermi energy modulated quantized Imbert-Fedorov shifts in Graphene`` accepted in Journal of the Optical Society of America B, (2021).

[9] Muzamil Shah and Muhammad Sajid, ``Surface state dependent giant quantized photonic spin Hall effect in a magnetic topological thin film`` under review in Physica E: Low-dimensional Systems and Nanostructures, (2021).

[10] Muzamil Shah and Muhammad Sabieh Anwar, ``dc and ac transport in two-dimensional ferrovalley materials,"in preparation (2021).

Abstract: 

Isolated quantum systems are an idealization - realistic quantum systems interact with their external environment. Due to these unavoidable interactions, such systems are generally subjected to decoherence and dissipation, which means that the quantum properties of the system are lost. Since upcoming powerful quantum technologies rely on the preservation of the quantum properties of systems, studying the dynamics of such open quantum systems has acquired immense importance. Unfortunately, this is generally a hard task, and various approximations have to be made to make the problem tractable. Usually, the most critical of these is that the system-environment coupling is weak. However, this may not be true in many different physical systems of interest. The central aim of the thesis is to look at open quantum systems beyond the usual weak coupling paradigm.

We first examine the role of the initial system-environment correlations by looking at an exactly solvable model involving a central two-level system coupled to a spin environment. We show that if the system-environment coupling is strong, then the initial system environment state cannot be considered to be a simple product state of the initial system state and the environment state. Rather, the correlations between the system and the environment that exist before the system state preparation procedure need to be taken into account. These correlations affect the environment state when the system state is prepared, and thus the subsequent dynamics of the system is also affected.

We then look at what happens to an open quantum system in the presence of repeated projective measurements. In particular, we look start by looking at non-selective projective measurements, that is, projective measurements where we do not care about the measurement result. We derive a general formalism that allows us to find the effective decay rate of a quantum state when it is subjected to periodic projective measurements for an arbitrary system-environment model. Importantly, we show that the decay rate with non-selective measurements is in general only different from the usual selective projective measurements scenario when we go beyond the weak system-environment coupling regime. Our formalism is applied to three exactly solvable models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems and a large spin undergoing dephasing in order to illustrate our results.

We next analyze the effect of repeated measurements on open quantum systems which are subjected to coherent driving fields. We assume that the system-environment coupling strength is weak; however, no such restriction is placed on the driving fields. We work out general expressions for the effective decay rate of a quantum system. We demonstrate that the driving fields change the decay rate for two-level system, both qualitatively and quantitatively. We also extend our results to systems consisting of more than one two-level system, as well as a two-level system strongly coupled to an environment of harmonic oscillators, to further illustrate the non-trivial effect of the driving  fields on the quantum Zeno and anti-Zeno effects.

Finally, we also consider the effect of repeated measurements on a quantum system interacting with a composite environment.  Here, the composite environment is made up of a single harmonic oscillator which is in turn weakly coupled to a collection of harmonic oscillators. We find interesting effects of varying the coupling strengths between the parts of the composite environment on effective decay rate of central system.

List of Publications 

M. Majeed and A. Z. Chaudhry, The quantum Zeno and anti-Zeno effects with non-selective projective measurements, Sci. Rep. 8, 14887 (2018).

M. Majeed and A. Z. Chaudhry, Effect of initial system-environment correlations with spin environments, Eur. J. Phys. D 73, 16 (2019).

M. Majeed and A. Z. Chaudhry, The quantum Zeno and anti-Zeno effects with driving fields in the weak and strong coupling regimes, Sci. Rep. 11, 1836 (2021).

M. Majeed and A. Z. Chaudhry, The quantum Zeno and anti-Zeno effects with composite environments, in preparation.

Abstract: 

This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for the practical implementation of modern quantum technologies. In studies of open quantum systems per- formed to date, a very common assumption is that the system and the environment are in separated initial states to begin with. One primary objective of this thesis is to critically analyse this assumption. As such, the core of this thesis incorporates the effect of the initial system-environment (SE) correlations that are present in the joint thermal equilibrium state of the system and the environment on the subsequent system dynamics. In this regard, we follow two different approaches to investigate the dynamics. First, we solve an exactly solvable spin-spin model where a central spin system interacts with a collection of quantum spins. We analyse exactly the central spin dynamics, starting from both initially correlated and uncorrelated SE states, and look at the dynamical differences due to the different starting states. Second, we consider an arbitrary system interacting with an arbitrary environment and derive a master equation that describes the system dynamics and also incorporates the effect of the initial SE correlations. This effect of initial correlations is captured by an extra term appearing in the master equation. The master equation is subsequently applied to the paradigmatic SE models such as the spin-boson model and the spin-spin model. We demonstrate that the role played by initial correlations can be noticeable even if the SE coupling strength is kept smaller.

 

The next part of the thesis deals with estimating the parameters characterizing the environment of a quantum system. After all, in order to predict the dynamics of a quantum system, one needs to know, for example, the cutoff frequency of the environment as well as its temperature. Recently, the use of a single qubit system to infer the characteristics of an environment has attracted considerable interest. We show that the use of two two-level systems can greatly enhance the estimation of the environment parameters. The reason is simple - two two-level systems also get correlated with each other due to their interactions with the environment, and information about the environment is imprinted onto these correlations. We quantitatively demonstrate this by calculating the quantum Fisher information for a two-qubit probe. Finally, in the last part of this thesis, we study the work counting statistics via a Markovian master equation for a periodically driven spin system weakly coupled to its environment of harmonic oscillators.

List of Publications:

Ali Raza Mirza, Muhammad Zia, and Adam Zaman Chaudhry “Master equation incorporating the system-environment correlations present in the joint equilib- rium state” published in Physical Review A, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.042205

Ali Raza Mirza, Mah Noor Jamil, and Adam Zaman Chaudhry “The role of initial system-environment correlations with a spin environment”, https://arxiv.org/abs/2301.07332.

Ali Raza Mirza and Adam Zaman Chaudhry “Improving the estimation of the environment parameters via a two-qubit scheme”, https://arxiv.org/abs/2305.12278.

Ali Raza Mirza and Ahsan Nazir “Work counting statistics in periodically driven strongly coulped quantum systems” (in progress).